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Dynamical variability, order-chaos transitions, and bursting Canards in the memristive Rulkov neuron model

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  • Bashkirtseva, I.
  • Ryashko, L.

Abstract

The problem of analyzing the mechanisms of variability in neural dynamics caused by memristive connections is considered. This problem is studied on the base of a neuron model combining the Rulkov map and discrete memristor. The extreme multistability of this 3D model is explained by the existence of a continuum family of invariant 2D planes. We show transformations of the system dynamics caused by an increase of the strength of magnetic induction current. Memristor-induced multistage transitions between order and chaos, resulting in formation of chaotic bursts through Canard explosion, are studied.

Suggested Citation

  • Bashkirtseva, I. & Ryashko, L., 2024. "Dynamical variability, order-chaos transitions, and bursting Canards in the memristive Rulkov neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008695
    DOI: 10.1016/j.chaos.2024.115317
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    References listed on IDEAS

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