Yuriy Rogovchenko

• Serkibayev, Dias; Zhakatayev, Altay & Rogovchenko, Yuriy (2025). Dynamic equations for an n-link planar pendulum in absolute and relative coordinate systems and computational efficiency. Nonlinear dynamics. ISSN 0924-090X. 114. doi: 10.1007/s11071-025-11862-1. Full text in Research Archive Show summary

  For a planar pendulum with an arbitrary number of links, we derive dynamic equations in a matrix–vector form in absolute and relative coordinate systems. This is done for four pendulum systems of increasing levels of complexity known for their rich dynamics: a simple mathematical pendulum, a mathematical pendulum with arbitrary mass location along the links, a physical pendulum, and a damped physical pendulum. We explore the influence of the choice of coordinate system on the computational performance during the forward integration of planar pendulums presented in two coordinate systems, absolute and relative, by comparing computation time and error. Simulation results for chaotic and smooth, damped and undamped, transient and steady-state-behavior pendulum systems are presented. They demonstrate that the use of dynamic equations in the absolute coordinate system requires less computational time and leads to a smaller error compared to the computations with the dynamic equations in the relative coordinate system. Our results emphasize the importance of the choice of the correct coordinate system for the description of a given dynamic system. The Denavit-Hartenberg convention is commonly used to compute forward kinematics. It systematically assigns coordinate frames to the links of a robot manipulator, utilizing the relative coordinate system, and reducing the number of parameters associated with reference frames to four. However, we demonstrate that this choice is not optimal in terms of computational efficiency.

• Zhakatayev, Altay; Rogovchenko, Yuriy & Pätzold, Matthias Uwe (2025). Global temporal observability of linear dynamic systems. IFAC Journal of Systems and Control. 32. doi: 10.1016/j.ifacsc.2025.100312. Full text in Research Archive Show summary

  In this paper, we introduce a new concept termed global temporal observability for continuous and discrete linear dynamic systems and explore its connection with the classical notion of observability. It is shown that, as a concept, global temporal observability is a generalization of the classical observability. However, as a feature of a dynamic system, global temporal observability is embedded into classical observability. The necessary condition for global temporal observability is presented. Four linear systems were considered to test the proposed concept. Since observability is a binary test, our results matched the results of classical observability analysis when appropriate basis functions are utilized. The advantages and disadvantages of the proposed concept are discussed. The main advantage of global temporal observability is that it restores the state function for the entire time duration in a single step that requires matrix inversion. It is shown that global temporal observability connects state reconstruction, differential equations, and observability concepts.

• Zhakatayev, Altay; Avazov, Nurilla; Najjar, Hasan; Rogovchenko, Yuriy & Pätzold, Matthias Uwe (2024). Blind parameter identification of implicit differential equations using the collocation discretization and homotopy optimization methods. Mechanism and Machine Theory. ISSN 0094-114X. 200. doi: 10.1016/j.mechmachtheory.2024.105715. Full text in Research Archive
• Martinez, Paul Hernandez; Rogovchenko, Svitlana; Rogovchenko, Yuriy & Treffert-Thomas, Stephanie (2024). “The theorem says…”: Engineering students making meaning of solutions to Ordinary Differential Equations. Journal of Mathematical Behavior. ISSN 0732-3123. 73. doi: 10.1016/j.jmathb.2023.101116. Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2024). Exactness: A Concept Important for Engineering Applications or a Source of Potential Difficulties? IEEE Transactions on Education. ISSN 0018-9359. 67(4), p. 562–573. doi: 10.1109/TE.2023.3335874. Full text in Research Archive
• Zhakatayev, Altay; Rogovchenko, Yuriy & Pätzold, Matthias Uwe (2023). Recursive inverse dynamics sensitivity analysis of open-tree-type multibody systems. Nonlinear dynamics. ISSN 0924-090X. 111, p. 11297–11313. doi: 10.1007/s11071-023-08433-7. Full text in Research Archive Show summary

  We present a first-order recursive approach to sensitivity analysis based on the application of the direct differentiation method to the inverse Lagrangian dynamics of rigid multibody systems. Our method is simple and efficient and is characterized by the following features. Firstly, it describes the kinematics of multibody systems using branch connectivity graphs and joint-branch connectivity matrices. For most mechanical systems with an open-tree kinematic structure, this method turns out to be more efficient compared to other kinematic descriptions employing joint or link connectivity graphs. Secondly, a recursive sensitivity analysis is presented for a dynamic system with an open-tree kinematic structure and inverse dynamic equations described in terms of the Lagrangian formalism. Thirdly, known approaches to recursive inverse dynamic and sensitivity analyses are modified to include dynamic systems with external forces and torques acting simultaneously at all joints. Finally, the proposed method for sensitivity analysis is easy to implement and computationally efficient. It can be utilized to evaluate the derivatives of the dynamic equations of multibody systems in gradient-based optimization algorithms. It also allows less experienced users to perform sensitivity analyses using the power of high-level programming languages such as MATLAB. To illustrate the method, simulation results for a human body model are discussed. The shortcomings of the method and possible directions for future work are outlined.

• Rogovchenko, Yuriy (2023). A Mathematical Modelling Project with Biology Undergraduates: Using Activity Theory to Understand Tensions. In Greefrath, Gilbert; Carreira, Sara Correia & Stillman, Gloria Ann (Ed.), Advancing and Consolidating Mathematical Modelling. Springer. ISSN 9783031271151. p. 177–192. doi: 10.1007/978-3-031-27115-1_11. Full text in Research Archive
• Holm, Kjetil Tengesdal; Rebenda, Josef & Rogovchenko, Yuriy (2023). Impact of Travel on Spread of Infection. In Pinto, Carla M. A. & Ionescu, Clara Mihaela (Ed.), Computational and Mathematical Models in Biology. Springer. ISSN 9783031426896. p. 183–211. doi: 10.1007/978-3-031-42689-6_8. Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2023). Identifying Tensions in a Small Group Work on an Open-Ended Modelling Task. Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education (RUME). p. 736–743. Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2023). Potential conflict factors in learning exact differential equations: Analysis of students’ work. In Drijvers, Paul; Csapodi, Csaba; Palmer, Hanna; Gosztonyi, Katalin & Kónya, Eszter (Ed.), Proceedings of the thirteenth Congress of the European Society for Research in Mathematics Education (CERME13). European Society for Research in Mathematics Education. ISSN 9789637031045. p. 2517–2524. Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2023). Mathematics education of future biologists: A strong need for brokering between mathematics and biology communities of practice. In Dreyfus, Tommy; Gonzalez-Martin, Alejandro S.; Monaghan, John David; Nardi, Elena & Thompson, Pat (Ed.), The learning and teaching of calculus across disciplines - proceedings of the second calculus conference. MatRIC. Full text in Research Archive
• Zhakatayev, Altay; Avazov, Nurilla; Rogovchenko, Yuriy & Pätzold, Matthias Uwe (2023). Human Motion Synthesis Using Trigonometric Splines. IEEE Access. 11, p. 14293–14308. doi: 10.1109/ACCESS.2023.3244062. Full text in Research Archive Show summary

  In this work, we present a simple framework to synthesize human motion. Our main goal is to propose a methodology tailored for inexperienced users to initiate their research in human motion simulation and human motion trajectory optimization. The novelties of the work include the following. First, trigonometric splines are used instead of traditional B-splines to discretize the generalized coordinates and velocities. Second, useful identities for trigonometric splines are derived. Third, this work is intended to be an example, so that even non-skilled users, such as undergraduate students, can perform human motion analysis using a high-level programming language such as MATLAB. Four simulations of human motion are generated: walking, sitting and standing, side-step, and jump. The results of the walking simulation are validated by experiments. Simulation and experimental results are presented and discussed.

• Hernandez-Martinez, Paul; Rogovchenko, Svitlana; Rogovchenko, Yuriy & Treffert-Thomas, Stephanie (2023). Collaboration between Mathematicians and Mathematics Educators: dialogical inquiry as a methodological tool in Mathematics Education research. Educational Studies in Mathematics. ISSN 0013-1954. 114, p. 129–148. doi: 10.1007/s10649-023-10245-w. Full text in Research Archive Show summary

  Collaboration between Mathematicians and Mathematics Educators is crucial in advancing knowledge on the teaching and learning of Mathematics, particularly in advanced Mathematics pedagogy. However, there is a need for the type of collaborations where Mathematicians and Mathematics Educators can find common ground, and the synergy of their expertise results in new, hybrid meanings and understandings that can benefit practice. This paper aims to help researchers from these communities come together by presenting a novel methodology for collaborative inquiry and qualitative data analysis—dialogical inquiry—based on Mikhail Bakhtin’s theory of dialogism. In this framework, “truth” is conceived as never finalised but always coevolving through dialogue that involves participants with different “voices” and “languages”. We describe the three principles that underpin dialogical inquiry: motivation, power balance and a process for solving disagreements. These three principles interact together to create a space where critically productive dialogue allows for meanings to coevolve and new, hybrid understandings to emerge. We illustrate our operationalisation of these principles (i.e., the methods of dialogical inquiry) in two areas: understanding solutions to linear ordinary differential equations and making meaning of the Bakhtinian concept of superaddressee. We reflect on our use of this methodology in Mathematics Education research and invite the readers to create their own dialogic spaces of collaboration.

• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2023). Mathematics education of future biologists: A strong need for brokering between mathematics and biology communities of practice. In Dreyfus, Tommy; Gonzalez-Martin, Alejandro S.; Monaghan, John David; Nardi, Elena & Thompson, Pat (Ed.), The learning and teaching of calculus across disciplines - proceedings of the second calculus conference. MatRIC. Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2022). Conceptual understanding of solutions to differential equations: How do assessment tasks promote it? In Hodgen, Jeremy; Geraniou, Eirini; Bolondi, Giorgio; Feretti, Federica & Ferretti, Federica (Ed.), Proceedings of the 12th Congress of the European Society for Research in Mathematics Education (CERME12). European Society for Research in Mathematics Education. ISSN 9791221025378. Full text in Research Archive
• Rezvanifard, Faezeh; Radmehr, Farzad & Rogovchenko, Yuriy (2022). Advancing engineering students' conceptual understanding through puzzle-based learning: a case study with exact differential equations. Teaching Mathematics and its Applications. ISSN 0268-3679. 42(2), p. 126–149. doi: 10.1093/teamat/hrac005. Full text in Research Archive Show summary

  Current views on the teaching of differential equations (DEs) are shifting towards the use of graphical and numerical methods. Motivated by recent research suggesting that puzzle-based learning (PzBL) can improve the teaching and learning of STEM subjects and by the lack of relevant studies for DEs, we designed two tasks—sophism and paradox—to explore undergraduate engineering students’ conceptual understanding of a classical topic—exact DEs—and to analyse the process of meaning-making during collaborative learning in small groups. One hundred and thirty-five undergraduate engineering students from a public university in Iran participated. In response to recent research signalling the tendency of the students to procedural learning of DEs, we analyse how the students in our study engaged in small group work on puzzle tasks, gaining a more conceptual understanding of exact DEs and acknowledging the efficiency of PzBL in their responses to a questionnaire and in interviews.

• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2022). Promoting conceptual understanding of differential equations through inquiry tasks. In Järvinen, Hannu-Matti; Silvestre, Santiago; Llorens, Ariadna & Nagy, Balázs (Ed.), Towards a new future in engineering education, new scenarios that European alliances of tech universities open up. Société européenne pour la formation des ingénieurs (SEFI). ISSN 9788412322262. Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2022). Promoting engineering students' learning with mathematical modelling projects. In Järvinen, Hannu-Matti; Silvestre, Santiago; Llorens, Ariadna & Nagy, Balázs (Ed.), Towards a new future in engineering education, new scenarios that European alliances of tech universities open up. Société européenne pour la formation des ingénieurs (SEFI). ISSN 9788412322262. Full text in Research Archive
• Zhakatayev, Altay; Rogovchenko, Yuriy & Pätzold, Matthias Uwe (2022). Synthesis of Lower-Body Human Walking using Trigonometric Spline Method, 2022 IEEE-RAS 21st International Conference on Humanoid Robots (Humanoids). IEEE (Institute of Electrical and Electronics Engineers). ISSN 9798350309799. p. 358–363. doi: 10.1109/Humanoids53995.2022.10000253. Full text in Research Archive Show summary

  In this work, preliminary results of human motion synthesis are presented. Specifically, a single stride motion (consisting of two steps) of a human lower-body model is obtained. The optimal control problem was reformulated as a nonlinear programming problem using the differential inclusion method. The main goal of this study is to compare the performance of trigonometric and polynomial (B-spline) discretization methods. The obtained results indicate that the trigonometric spline method performs similarly to the B-spline method and results in a smooth motion.

• Hernandez-Martinez, Paul; Thomas, Stephanie; Viirman, Olov Lui & Rogovchenko, Yuriy (2021). ‘I’m still making dots for them’: mathematics lecturers’ views on their mathematical modelling practices. International Journal of Mathematical Education in Science and Technology. ISSN 0020-739X. 52(2), p. 165–177. doi: 10.1080/0020739X.2019.1668977. Full text in Research Archive Show summary

  Using Cultural-Historical Activity Theory, we analyze lecturers’ views on the aims and teaching practices of mathematical modelling (MM) education in Norway and England. We aim to expose the tensions that exist within the activity of teaching MM at university, such as those between multiple, sometimes competing, aims for teaching MM, or between the lecturers’ professional identities and the structure of university degrees. Our conceptualization of these tensions might help lecturers consider how to overcome obstacles in their own contexts.

• Rogovchenko, Yuriy; Astafieva, Mariia; Martinez, Paul Hernandez; Lytvyn, Oksana; Morze, Nataliia & Pátíková, Zuzana [Show all 8 contributors for this article] (2021). Mathematical Modelling and Inquiry-Based Mathematics Education, Inquiry in University Mathematics Teaching and Learning. The Platinum Project. Nakladatelství Masarykovy univerzity. ISSN 9788021099838. p. 147–170. doi: 10.5817/CZ.MUNI.M210-9983-2021-8. Full text in Research Archive Show summary

  Mathematical modelling (MM) is a powerful tool used by scientists and engineers to solve important problems for humankind. MM opens many possibilities for inquiry and has been included in the PLATINUM project as one of the Intellectual Outputs, IO5 (see Chapter 5 for the complete list). We consider MM an important part of the teaching and learning process. We believe that helping to develop students’ modelling competencies we equip them with a valuable understanding of practical and theoretical concepts, prepare them for a life-long learning, and form them as critical citizens. This chapter is organised as follows. In Section 8.2, we share our views on why we teach MM, noting that our teaching practices are adapted differently to suit local educational contexts (types of students, programs of study, institutional traditions, constraints, etc.). We proceed with the discussion of what are the most important to us characteristics of Inquiry-Based Mathematics Education (IBME) as a teaching approach. To explain authors’ understanding of how the MM relates to IBME, the concept of ‘active knowledge’ is introduced in Section 8.3. The key idea of this concept is that in response to the use of IBME in the classroom students’ engagement with MM activates previously acquired knowledge and facilitates its efficient use. In Section 8.4, partners present examples of the use of MM within IBME practices and comment on how students activate their mathematical knowledge. Each example shows multifaceted connections between MM and IBME. We reflect on the lessons learned from our contributions to the Intellectual Output IO5 in Section 8.5

• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2021). Teaching Students to Think Mathematically Through Inquiry: The Norwegian Experience, Inquiry in University Mathematics Teaching and Learning. The Platinum Project. Nakladatelství Masarykovy univerzity. ISSN 9788021099838. p. 197–213. doi: 10.5817/CZ.MUNI.M210-9983-2021-11. Full text in Research Archive
• Rogovchenko, Yuriy & Rebenda, Josef (2021). Origins and Implementation of the Project, Inquiry in University Mathematics Teaching and Learning. The Platinum Project. Nakladatelství Masarykovy univerzity. ISSN 9788021099838. p. 73–92. doi: 10.5817/CZ.MUNI.M210-9983-2021-5. Full text in Research Archive Show summary

  The main theme of the book about the PLATINUM project is inquiry-based mathematics education and, in general, inquiry as a form of exploration and discovery in the classroom. In this chapter, we inquire into the following important issue: How did it happen that the project became the reality? How did the project evolve and what was its impact on the individuals who worked together on the project? It is not very common to see mathematicians and mathematics educators collaborate productively in a large-scale joint educational project (see Mohn, 2018). Therefore, we would like to provide the reader with an honest insiders’ account of what might bring mathematicians and mathematics educators to the collaboration in a joint project about teaching and learning mathematics. Our narrative might surprise those who believe that a project should always start with a concrete idea—for us it did not begin with an idea, our starting point was a heterogeneous group of university teachers and researchers interested in the collaboration in a project on university mathematics teaching. At the outset, let us briefly review the key characteristics of the PLATINUM project.

• Rogovchenko, Yuriy (2021). Mathematical Modelling with Biology Undergraduates: Balancing Task Difficulty and Level of Support. In Leung, Frederick Koon Shing; Stillman, Gloria A.; Kaiser, Gabriele & Wong, Ka Lok (Ed.), Mathematical modelling education in East and West. Springer. ISSN 9783030669959. p. 571–582. doi: 10.1007/978-3-030-66996-6_48. Full text in Research Archive
• Balyk, Nadiia; Vasylenko, Yaroslav; Grod, I.; Oleksiuk, Vasyl & Rogovchenko, Yuriy (2021). Project-based learning in a computer modelling course. Journal of Physics: Conference Series (JPCS). ISSN 1742-6588. 1840. doi: 10.1088/1742-6596/1840/1/012032. Full text in Research Archive
• Zhakatayev, Altay; Rogovchenko, Yuriy & Pätzold, Matthias Uwe (2021). Influence of generalized coordinates on system dynamics. In Kövecses, József; Stépán, Gábor & Zelei, Ambrus (Ed.), Proceedings of the 10th ECCOMAS Thematic Conference on MULTIBODY DYNAMICS. Budapest University of Technology and Economics. ISSN 9789634218708. p. 235–244. doi: 10.3311/ECCOMASMBD2021-112. Full text in Research Archive Show summary

  We investigate the effect of the choice of a set of generalized coordinates (GCs) on the simulation of the behavior of the dynamical system using the single-link spherical pendulum as an example. Specifically, we focus our attention on numerical errors and the simulation time necessary to simulate system dynamics. The Lagrangian method is applied to obtain the equations of motion. The generalized Euler angles are used as GCs. The GCs depend on the direction of the axes along which they are defined. Therefore, by parameterizing the directions of these two axes, different sets of GCs with the corresponding system of nonlinear differential equations are obtained. For a spherical pendulum, we demonstrate that the optimal sets of GCs leading to the minimum simulation time are orthogonal sets. However, contrary to our expectations, orthogonal sets do not result in the minimum simulation error. Additionally, the intrinsic generalized Euler angles lead to faster simulations than the extrinsic ones. Therefore, different choices of GCs are not equivalent from a numerical point of view and further research is needed to develop a strategy for selecting an optimal set of GCs.

• Rogovchenko, Yuriy; Viirman, Olov Lui & Treffert-Thomas, Stephanie (2020). Joy of Mathematical Modelling: A Forgotten Perspective? In Stillman, Gloria A.; Kaiser, Gabriele & Lampen, Christine Erna (Ed.), Mathematical Modelling Education and Sense-making. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer Nature. ISSN 9783030376727. p. 95–106. doi: 10.1007/978-3-030-37673-4_9. Full text in Research Archive Show summary

  We argue the relevance of including an affective perspective in the mathematical modelling education research and emphasise its importance for the teaching and learning of mathematical modelling at all levels, especially at the university. Our argument is supported by a recent survey of mathematics lecturers’ views on mathematical modelling, several follow-up interviews, and a review of literature on mathematical modelling that relates to enjoyment, pleasure, and appreciation. Findings from the survey and the follow-up interviews indicate that there is a group of practitioners who hold strong views on the importance of enjoyment in doing and teaching mathematical modelling.

• Rogovchenko, Yuriy (2020). Using Activity Theory to Understand Tensions in an Extra-Curricular Mathematical Modeling Project with Biology Undergraduates. Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education (RUME). p. 1236–1237. Full text in Research Archive Show summary

  We use activity theory to analyze tensions manifested in an activity system of an extracurricular mathematical modeling (MM) project with biology undergraduates at a research intense Scandinavian university. We present the evidence that the use of MM in education of biology students accentuates conceptual understanding of mathematics and may lead to beneficial shifts in pedagogical practice.

• Rogovchenko, Svitlana; Rogovchenko, Yuriy & Treffert-Thomas, Stephanie (2020). The Use of Nonstandard Problems in an Ordinary Differential Equations Course for Engineering Students Reveals Commognitive Conflicts. Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education (RUME). p. 1141–1145. Full text in Research Archive Show summary

  We report on a teaching intervention in an ordinary differential equations (ODEs) course for engineering students focusing our attention on the role of nonstandard problems in the challenging traditional approaches to Existence and Uniqueness Theorems (EUTs). Our analysis of the students mathematical discourse developed in the process of group discussions within Commognition Theoretical Framework reveals unresolved commognitive conflict. We suggest how modifications in the problem design prompted by the students mathematical discourse can be used to improve students conceptual understanding of the material.

• Li, Tongxing & Rogovchenko, Yuriy (2020). On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations. Applied Mathematics Letters. ISSN 0893-9659. 105. doi: 10.1016/j.aml.2020.106293. Full text in Research Archive Show summary

  By using comparison principles, we analyze the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations. Due to less restrictive assumptions on the coefficients of the equation and on the deviating argument, our criteria improve a number of related results reported in the literature.

• Duarte, Jorge; Januário, Cristina; Martins, Nuno; Rogovchenko, Svitlana & Rogovchenko, Yuriy (2019). Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic model. Journal of Mathematical Biology. ISSN 0303-6812. 78, p. 2235–2258. doi: 10.1007/s00285-019-01342-7. Full text in Research Archive Show summary

  Despite numerous studies of epidemiological systems, the role of seasonality in the recurrent epidemics is not entirely understood. During certain periods of the year incidence rates of a number of endemic infectious diseases may fluctuate dramatically. This influences the dynamics of mathematical models describing the spread of infection and often leads to chaotic oscillations. In this paper, we are concerned with a generalization of a classical Susceptible–Infected–Recovered epidemic model which accounts for seasonal effects. Combining numerical and analytic techniques, we gain new insights into the complex dynamics of a recurrent disease influenced by the seasonality. Computation of the Lyapunov spectrum allows us to identify different chaotic regimes, determine the fractal dimension and estimate the predictability of the appearance of attractors in the system. Applying the homotopy analysis method, we obtain series solutions to the original nonautonomous SIR model with a high level of accuracy and use these approximations to analyze the dynamics of the system. The efficiency of the method is guaranteed by the optimal choice of an auxiliary control parameter which ensures the rapid convergence of the series to the exact solution of the forced SIR epidemic model.

• Liakos, Yannis; Rogovchenko, Svitlana & Rogovchenko, Yuriy (2018). A New Tool for the Assessment of the Development of Students’ Mathematical Competencies, The 19th SEFI Mathematics Working Group Seminar on Mathematics in Engineering Education. European Society for Engineering Education. ISSN 9782873520175. p. 158–163. Full text in Research Archive
• Rogovchenko, Svitlana; Treffert-Thomas, Stephanie & Rogovchenko, Yuriy (2018). Non-standard Problems in an Ordinary Differential Equations Course. International Network for Didactic Research in University Mathematics : INDRUM. Full text in Research Archive
• Pasic, Mervan & Rogovchenko, Yuriy (2018). Global Non-monotonicity of Solutions to Nonlinear Second-Order Differential Equations. Mediterranean Journal of Mathematics. ISSN 1660-5446. 15(2). doi: 10.1007/s00009-018-1075-2. Full text in Research Archive
• Rogovchenko, Svitlana; Rogovchenko, Yuriy & Treffert-Thomas, Stephanie (2018). The use of nonstandard problems in an ODE course for engineering students. Proceedings of the International Groups for the Psychology of Mathematics Education. ISSN 0771-100X. 4, p. 283–290. Full text in Research Archive
• Hernandez-Martinez, Paul; Viirman, Olov Lui; Treffert-Thomas, Stephanie & Rogovchenko, Yuriy (2017). Mathematics lecturers’ views on the teaching of mathematical modelling. NOMAD – Nordisk matematikkdidaktikk. ISSN 1104-2176. 22(4), p. 121–145. Full text in Research Archive
• Li, Tongxing & Rogovchenko, Yuriy (2017). Oscillation criteria for second-order superlinear Emden?Fowler neutral differential equations. Monatshefte für Mathematik (Print). ISSN 0026-9255. 184(3), p. 489–500. doi: 10.1007/s00605-017-1039-9. Full text in Research Archive
• Li, Tongxing & Rogovchenko, Yuriy (2017). On asymptotic behavior of solutions to higher-order sublinear Emden–Fowler delay differential equations. Applied Mathematics Letters. ISSN 0893-9659. 67, p. 53–59. doi: 10.1016/j.aml.2016.11.007. Full text in Research Archive
• Viirman, Olov Lui; Goodchild, Simon & Rogovchenko, Yuriy (2016). Using mathematical modelling activities to motivate biology students to learn mathematics. In Csíkos, Csaba; Rausch, Attila & Szitányi, Judit (Ed.), Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education. PME. ISSN 9781365463389. p. 262–262. Full text in Research Archive
• Li, Tongxing & Rogovchenko, Yuriy (2016). Oscillation criteria for even-order neutral differential equations. Applied Mathematics Letters. ISSN 0893-9659. 61, p. 35–41. doi: 10.1016/j.aml.2016.04.012. Full text in Research Archive
• Li, Tongxing & Rogovchenko, Yuriy (2015). Oscillation of second-order neutral differential equations. Mathematische Nachrichten. ISSN 0025-584X. 288(10), p. 1150–1162. doi: 10.1002/mana.201300029. Full text in Research Archive
• Li, Tongxing; Rogovchenko, Yuriy & Zhang, Chengchui (2015). Oscillation of fourth-order quasilinear differential equations. Mathematica Bohemica. ISSN 0862-7959. 140(4), p. 405–418. doi: 10.21136/mb.2015.144459. Full text in Research Archive
• Li, Tongxing & Rogovchenko, Yuriy (2014). Oscillation Theorems for Second-Order Nonlinear Neutral Delay Differential Equations. Abstract and Applied Analysis. ISSN 1085-3375. 2014. doi: 10.1155/2014/594190. Full text in Research Archive Show summary

  We analyze the oscillatory behavior of solutions to a class of second-order nonlinear neutral delay differential equations. Our theorems improve a number of related results reported in the literature.

• Li, Tongxing & Rogovchenko, Yuriy (2014). Asymptotic behavior of higher-order quasilinear neutral differential equations. Abstract and Applied Analysis. ISSN 1085-3375. 2014:395368. doi: 10.1155/2014/395368. Full text in Research Archive Show summary

  We study asymptotic behavior of solutions to a class of higher-order quasilinear neutral differential equations under the assumptions that allow applications to even- and odd-order differential equations with delayed and advanced arguments, as well as to functional differential equations with more complex arguments that may, for instance, alternate indefinitely between delayed and advanced types. New theorems extend a number of results reported in the literature. Illustrative examples are presented.

• Rogovchenko, Yuriy & Li, Tongxing (2014). Oscillatory Behavior of Second-Order Nonlinear Neutral Differential Equations. Abstract and Applied Analysis. ISSN 1085-3375. 2014. doi: 10.1155/2014/143614. Full text in Research Archive Show summary

  We study oscillatory behavior of solutions to a class of second-order nonlinear neutral differential equations under the assumptions that allow applications to differential equations with delayed and advanced arguments. New theorems do not need several restrictive assumptions required in related results reported in the literature. Several examples are provided to show that the results obtained are sharp even for second-order ordinary differential equations and improve related contributions to the subject.

• Li, Tongxing; Rogovchenko, Yuriy & Tang, Shuhong (2014). Oscillation of second-order nonlinear differential equations with damping. Mathematica Slovaca. ISSN 0139-9918. 64(5), p. 1227–1236. doi: 10.2478/s12175-014-0271-1. Full text in Research Archive
• Li, Tongxing & Rogovchenko, Yuriy (2014). Asymptotic behavior of an odd-order delay differential equation. Boundary Value Problems. ISSN 1687-2762. 2014:107. doi: 10.1186/1687-2770-2014-107. Full text in Research Archive Show summary

  We study asymptotic behavior of solutions to a class of odd-order delay differential equations. Our theorems extend and complement a number of related results reported in the literature. An illustrative example is provided.

• Li, Tongxing; Rogovchenko, Yuriy & Zhang, Chenghui (2013). Oscillation results for second-order nonlinear neutral differential equations. Advances in Difference Equations. ISSN 1687-1839. doi: 10.1186/1687-1847-2013-336. Full text in Research Archive Show summary

  We obtain several oscillation criteria for a class of second-order nonlinear neutral differential equations. New theorems extend a number of related results reported in the literature and can be used in cases where known theorems fail to apply. Two illustrative examples are provided.

• Hasanbulli, Mustafa; Rogovchenko, Svitlana P. & Rogovchenko, Yuriy (2013). Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting. Journal of Applied Mathematics. ISSN 1110-757X. 2013. doi: 10.1155/2013/167671. Full text in Research Archive Show summary

  We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was studied by Brauer and Sanchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. We obtain estimates for positive attracting and repelling periodic solutions and describe behavior of other solutions. Extinction and blow-up times are evaluated for solutions with small and large initial data; dependence of the number of periodic solutions on the parameter sigma associated with the intensity of harvesting is explored. As sigma grows, the number of periodic solutions drops from two to zero. We provide bounds for the bifurcation parameter whose value in practice can be efficiently approximated numerically.

• Li, Tongxing; Rogovchenko, Yuriy & Zhang, Chenghui (2013). Oscillation of Second-Order Neutral Differential Equations. Funkcialaj Ekvacioj. ISSN 0532-8721. 56(1), p. 111–120. doi: 10.1619/fesi.56.111. Full text in Research Archive

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• Rogovchenko, Yuriy; Rogovchenko, Svitlana & Thomas, Stephanie (2018). Bergquist, Österholm M, Granberg, Sumpter L. Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 4). Umeå, Sweden: International Group for the psychology of Mathematics Education. ISBN 978-91-7601-905-4. International Group for the Psychology of Mathematics Education. ISBN 9789176019054. 485 p. Full text in Research Archive

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• Cristea, Irina; Siarry, Patrick; Dzemyda, Gintautas & Rogovchenko, Yuriy (2024). Preface to the Special Issue “State-of-the-Art Mathematical Applications in Europe”. Mathematics. 12(14). doi: 10.3390/math12142161. Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2023). Students’ Difficulties with the Understanding of the Concept of the General Solution to a Differential Equation: Can We Teach It Better? Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2023). Identifying Tensions in a Small Group Work on an Open-Ended Modelling Task. Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2023). Mathematical modeling projects in advanced ordinary differential equations courses for mathematics and engineering students. Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2023). Mathematical model of yeast growth: biology students use mathematics to understand biological processes. Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2023). Mathematics education of future biologists: A strong need for brokering between mathematics and biology communities of practice. Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2023). Students’ Difficulties with the Understanding of the Concept of the General Solution to a Differential Equation: Can We Teach It Better? Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2023). Potential conflict factors in learning exact differential equations: Analysis of students’ work. Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2022). Conceptual understanding of solutions to differential equations: How do assessment tasks promote it? Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2022). Conceptual understanding of solutions to differential equations: How do assessment tasks promote it? Full text in Research Archive
• Rogovchenko, Yuriy & Rogovchenko, Svitlana (2022). Promoting conceptual understanding of differential equations through inquiry tasks. Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2022). Potential conflict factors in learning exact differential equations: an impact of institutional practices. Full text in Research Archive
• Rogovchenko, Svitlana & Rogovchenko, Yuriy (2022). Promoting engineering students' learning with mathematical modelling projects. Full text in Research Archive
• Rogovchenko, Yuriy (2020). Using Activity Theory to Understand Tensions in an Extra-Curricular Mathematical Modeling Project with Biology Undergraduates. Full text in Research Archive Show summary

  We use activity theory to analyze tensions manifested in an activity system of an extracurricular mathematical modeling (MM) project with biology undergraduates at a research intense Scandinavian university. We present the evidence that the use of MM in education of biology students accentuates conceptual understanding of mathematics and may lead to beneficial shifts in pedagogical practice.

• Rogovchenko, Svitlana; Rogovchenko, Yuriy & Treffert-Thomas, Stephanie (2020). The Use of Nonstandard Problems in an Ordinary Differential Equations Course for Engineering Students Reveals Commognitive Conflicts. Full text in Research Archive
• Rogovchenko, Yuriy & Vos, Pauline (2019). MERGA Strand 2 - The teaching & learning of Mathematics in non-mathematical practices. Full text in Research Archive
• Rogovchenko, Yuriy (2019). Mathematical modelling activity with biology undergraduates. Full text in Research Archive
• Thomas, Stephanie; Rogovchenko, Svitlana & Rogovchenko, Yuriy (2018). THE USE OF NONSTANDARD PROBLEMS IN AN ODE COURSE FOR ENGINEERING STUDENTS. Full text in Research Archive
• Rogovchenko, Svitlana; Rogovchenko, Yuriy & Thomas, Stephanie (2018). Non-standard Problems in an Ordinary Differential Equations Course. Full text in Research Archive
• Liakos, Ioannis Evagellos & Rogovchenko, Yuriy (2018). Assessing the Development of Students’ Mathematical Modeling Competencies: An Information Entropy Approach. Full text in Research Archive
• Liakos, Ioannis Evagellos; Rogovchenko, Svitlana & Rogovchenko, Yuriy (2018). A New Tool for the Assessment of the Development of Students' Mathematical Competencies. Full text in Research Archive
• Thomas, Stephanie; Rogovchenko, Svitlana & Rogovchenko, Yuriy (2018). Development of Students Mathematical Discourse through Individual and Group Work with Nonstandard Problems on Existence and Uniqueness Theorems. Full text in Research Archive
• Goodchild, Simon; Viirman, Olov Lui & Rogovchenko, Yuriy (2017). An inquiry based approach to the development of a mathematical modelling infused curriculum for biology students. Full text in Research Archive
• Rogovchenko, Svitlana; Rogovchenko, Yuriy & Treffert-Thomas, Stephanie (2017). Individual and Group Work with Nonstandard Problems in an ODE course for Engineering Students. Full text in Research Archive
• Rogovchenko, Yuriy & Li, Tongxing (2017). Oscillation criteria for second-order neutral differential equations. Full text in Research Archive
• Viirman, Olov Lui; Hernandez-Martinez, Paul; Treffert-Thomas, Stephanie & Rogovchenko, Yuriy (2017). Joy of mathematical modelling: a forgotten perspective? Full text in Research Archive
• Viirman, Olov Lui; Goodchild, Simon & Rogovchenko, Yuriy (2016). Using mathematical modelling activities to motivate biology students to learn mathematics. Full text in Research Archive
• Li, Tongxing; Bohner, Marc; Candan, Tuncay; Rogovchenko, Yuriy & Wang, Qi-Ru (2016). Qualitative theory of differential equations, difference equations, and dynamic equations on time scales. Scientific World Journal. 2016:9094613, p. 1–2. doi: 10.1155/2016/9094613. Full text in Research Archive
• Viirman, Olov Lui; Goodchild, Simon & Rogovchenko, Yuriy (2015). Using mathematical modelling activities to motivate biology students to learn mathematics. Full text in Research Archive
• Rogovchenko, Yuriy (2015). Sammen om å utdanne fremtidens biologer. [Journal]. SFU magasinet. Full text in Research Archive
• Li, Tongxing; Diblík, Josef; Domoshnitsky, Alexander; Rogovchenko, Yuriy; Sadyrbaev, Felix & Wang, Qi-Ru (2015). Qualitative Analysis of Differential, Difference Equations, and Dynamic Equations on Time Scales. Abstract and Applied Analysis. ISSN 1085-3375. 2015. doi: 10.1155/2015/643706. Full text in Research Archive
• Diblík, Josef; Braverman, Elena; Györi, István; Rogovchenko, Yuriy; Ruzicková, Miroslava & Zafer, Agacik (2014). Functional Differential and Difference Equations with Applications 2013. Abstract and Applied Analysis. ISSN 1085-3375. 2014, p. 1–2. doi: 10.1155/2014/543797. Full text in Research Archive
• Rogovchenko, Yuriy (2014). Review on the book "The Universe in Zero Words. The story of mathematics as told through equations" by Dana Mackenzie. EMS Newsletter. ISSN 1027-488X. p. 57–57. Full text in Research Archive
• Rogovchenko, Yuriy; Su, Hua; Sang, Yanbin; Xu, Fuyi & Raffoul, Youssef (2013). Nonlinear functional difference equations with applications. Discrete Dynamics in Nature and Society. ISSN 1026-0226. doi: 10.1155/2013/360860. Full text in Research Archive
• Diblík, Josef; Braverman, Elena; Györi, István; Rogovchenko, Yuriy; Ruzicková, Miroslava & Zafer, Agacik (2012). Functional Differential and Difference Equations with Applications. Abstract and Applied Analysis. ISSN 1085-3375. 2012. doi: 10.1155/2012/986585. Full text in Research Archive
• Hernandez-Martinez, Paul; Treffert-Thomas, Stephanie; Rogovchenko, Yuriy & Viirman, Olov Lui (2016). Mathematics Lecturers' Views on the Teaching of Mathematical Modelling. MatRIC. Full text in Research Archive

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