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State transitions in the Morris-Lecar model under stable Lévy noise

Author

Listed:
  • Rui Cai

    (School of Science, Hubei University of Technology
    Center for Mathematical Sciences, Huazhong University of Science and Technology)

  • Yancai Liu

    (Center for Mathematical Sciences, Huazhong University of Science and Technology
    School of Mathematics and Statistics, Huazhong University of Science and Technology)

  • Jinqiao Duan

    (Illinois Institute of Technology)

  • Almaz Tesfay Abebe

    (Center for Mathematical Sciences, Huazhong University of Science and Technology
    School of Mathematics and Statistics, Huazhong University of Science and Technology
    Mekelle University)

Abstract

This work is about the state transition of the stochastic Morris-Lecar neuronal model driven by symmetric α-stable Lévy noise. The considered system is bistable: a stable equilibrium (resting state) and a stable limit cycle (oscillating state), and there is an unstable limit cycle (borderline state) between them. Small disturbances may cause a transition between the two stable states, thus a deterministic quantity, namely the maximal likely trajectory, is used to analyze the transition phenomena in a non-Gaussian stochastic environment. According to the numerical experiment, we find that smaller jumps of the Lévy motion and smaller noise intensities can promote such transition from the sustained oscillating state to the resting state. It also can be seen that larger jumps of the Lévy motion and higher noise intensities are conducive for the transition from the borderline state to the sustained oscillating state. As a comparison, Brownian motion is also taken into account. The results show that whether it is the oscillating state or the borderline state, the system disturbed by Brownian motion will be transferred to the resting state under the selected noise intensity with a high probability. Graphical abstract

Suggested Citation

  • Rui Cai & Yancai Liu & Jinqiao Duan & Almaz Tesfay Abebe, 2020. "State transitions in the Morris-Lecar model under stable Lévy noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(3), pages 1-9, March.
    • Handle: RePEc:spr:eurphb:v:93:y:2020:i:3:d:10.1140_epjb_e2020-100422-2
    DOI: 10.1140/epjb/e2020-100422-2
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    Cited by:

    1. Sebastian Jenderny & Karlheinz Ochs & Philipp Hövel, 2023. "A memristor-based circuit approximation of the Hindmarsh–Rose model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(8), pages 1-10, August.
    2. Shen, Zhuan & Zhang, Honghui & Du, Lin & Deng, Zichen & Kurths, Jürgen, 2023. "Initiation and termination of epilepsy induced by Lévy noise: A view from the cortical neural mass model," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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    Keywords

    Statistical and Nonlinear Physics;

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