Dynamical analysis of the Rulkov model with quasiperiodic forcing

Gaolei Li, Jicheng Duan, Zhixuan Yue, Zhe Li and Denghui Li

Chaos, Solitons & Fractals, 2024, vol. 189, issue P1

Abstract: This paper investigates the dynamical behavior of the Rulkov neuron model under quasiperiodic forcing, focusing on the emergence and mechanisms of strange nonchaotic attractors (SNAs). SNAs are characterized by fractal geometry without sensitive dependence on initial conditions, and their formation mechanisms, such as torus-doubling, fractal, bubble, Heagy–Hammel, and multi-intermittency routes, are explored in detail. The study employs Lyapunov exponents, singular continuous spectrum, and phase sensitivity to detect and characterize the strange and nonchaotic properties of attractors. Numerical simulations reveal the transition dynamics between strange nonchaotic, quasiperiodic, and chaotic states, emphasizing the role of transient dynamics in understanding the complex behavior of neural systems under multifrequency stimuli. The findings provide deeper insights into the intricate dynamical processes in neuron models, potentially aiding the development of advanced models for neural response prediction in varying environments.

Keywords: Quasiperiodically forced system; Strange nonchaotic attractor; Transient dynamics; Lyapunov exponents; Phase sensitivity (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924011573

DOI: 10.1016/j.chaos.2024.115605

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