Most probable trajectories of a birhythmic oscillator under random perturbations.

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2024-12-01 DOI:10.1063/5.0229131
Wenting Zhang, Wei Xu, Yaning Tang, Jürgen Kurths
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引用次数: 0

Abstract

This study investigates the most probable trajectories of a birhythmic oscillator under stochastic perturbations. The distinctive feature of the birhythmic oscillator is the coexistence of two stable limit cycles with different amplitudes and frequencies, separated by an unstable limit cycle. The path integral method was utilized to compute the instantaneous probability density. Based on the theory of most probable dynamics, by maximizing the probability density function, we present the time series of the most probable trajectories starting from different initial states. Furthermore, we conducted a detailed analysis of the noise-induced transitions between the two stable limit cycles under different parameter conditions. This approach enables us to understand and track the most probable escape time and specific most probable trajectories as the system transitions from the basin of attraction of one stable limit cycle to another. This work visualizes the most probable trajectories in stochastic systems and provides an innovative solution to the complex problem of noise-induced transitions between two stable limit cycles. Our research aims to provide a new perspective for studying complex stochastic dynamical systems.

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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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