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Bifurcation Analysis of the Topp Model

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Current Trends in Analysis, its Applications and Computation

Part of the book series: Trends in Mathematics ((RESPERSP))

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Abstract

In this paper, we study the 3-dimensional Topp model for the dynamics of diabetes. We show that for suitable parameter values an equilibrium of this model bifurcates through a Hopf-saddle-node bifurcation. Numerical analysis suggests that near this point Shilnikov homoclinic orbits exist. In addition, chaotic attractors arise through period doubling cascades of limit cycles.

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Acknowledgements

The authors thank Prof. Robert MacKay (University of Warwick, UK) who initiated this research. The first author was supported by the London Mathematical Society (LMS) and the Netherlands Organization for Scientific Research (NWO).

Author information

Authors and Affiliations

  1. National Academy of Sciences of Belarus, United Institute of Informatics Problems, Minsk, Belarus

    Valery A. Gaiko

  2. University of Groningen, Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, Groningen, The Netherlands

    Alef E. Sterk & Henk W. Broer

Authors
  1. Valery A. Gaiko
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  2. Alef E. Sterk
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  3. Henk W. Broer
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Paula Cerejeiras

  2. Institut of Applied Analysis, TU Bergakademie Freiberg, Freiberg, Germany

    Michael Reissig

  3. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Irene Sabadini

  4. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Joachim Toft

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Gaiko, V.A., Sterk, A.E., Broer, H.W. (2022). Bifurcation Analysis of the Topp Model. In: Cerejeiras, P., Reissig, M., Sabadini, I., Toft, J. (eds) Current Trends in Analysis, its Applications and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-87502-2_1

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