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Dynamics of a Reduced System Connected to the Investigation of an Infinite Network of Identical Theta Neurons

Author

Listed:
  • Lavinia Bîrdac

    (Department of Mathematics and Computer Science, West University of Timişoara, 300223 Timişoara, Romania
    These authors contributed equally to this work.)

  • Eva Kaslik

    (Department of Mathematics and Computer Science, West University of Timişoara, 300223 Timişoara, Romania
    Institute for Advanced Environmental Research, West University of Timişoara, 300223 Timişoara, Romania
    These authors contributed equally to this work.)

  • Raluca Mureşan

    (Department of Mathematics and Computer Science, West University of Timişoara, 300223 Timişoara, Romania
    These authors contributed equally to this work.)

Abstract

We consider an infinite network of identical theta neurons, all-to-all coupled by instantaneous synapses. Using the Watanabe–Strogatz Ansatz, the mathematical model of this infinite network is reduced to a two-dimensional system of differential equations. We determine the number of equilibria of this reduced system with respect to two characteristic parameters. Furthermore, we discuss the stability properties of each equilibrium and the possible bifurcations that may take place. As a result, the occurrence of exotic higher codimension bifurcations involving a degenerate center is also unveiled. Numerical results are also presented to illustrate complex dynamic behaviour in the reduced system.

Suggested Citation

  • Lavinia Bîrdac & Eva Kaslik & Raluca Mureşan, 2022. "Dynamics of a Reduced System Connected to the Investigation of an Infinite Network of Identical Theta Neurons," Mathematics, MDPI, vol. 10(18), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3245-:d:908825
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    References listed on IDEAS

    as
    1. Llibre, Jaume & Pantazi, Chara, 2016. "Limit cycles bifurcating from a degenerate center," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 120(C), pages 1-11.
    2. Bei Chen & Xinxin Cheng & Han Bao & Mo Chen & Quan Xu, 2022. "Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator," Mathematics, MDPI, vol. 10(5), pages 1-13, February.
    Full references (including those not matched with items on IDEAS)

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