Noise-induced chaos and generation of phantom attractors in a birhythmic neuron model

Lev Ryashko and Irina Bashkirtseva

Chaos, Solitons & Fractals, 2025, vol. 191, issue C

Abstract: We analyze mechanisms of stochastic transformations of complex oscillatory regimes in the 2D Rulkov model with the smooth map. In the birhythmicity parametric zone with coexistence of periodic and chaotic oscillations, noise-induced transitions from regular spiking to chaotic bursting are studied. In the monorhythmicity zone of regular periodic oscillations, the stochastic phenomenon of the systematic shift of probability distributions with generation of a phantom chaotic attractor is discovered and analyzed. The relationship of this phenomenon with the presence of transient chaotic attractors in the original deterministic model is revealed and discussed. For parametric analysis of these phenomena, we apply the confidence ellipses method based on the stochastic sensitivity technique.

Keywords: Birhythmicity; Rulkov neuron model; Spiking; Chaotic bursting; Noise-induced transformations; Order-chaos transitions; Phantom attractor; Confidence ellipses (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924013936

DOI: 10.1016/j.chaos.2024.115841

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