Chaotic stochastic resonance in Mackey-Glass equations

2025/05/08 by Eiki Kojima, Yuzuru Sato, Kojima, Eiki +1 · 1 voice
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #advanced mathematical theories #nlin.CD

paper · pdf · doi:10.48550/arxiv.2505.04874

openalex publication_date 2025/05/08 · arxiv published 2025/05/08 · openalex created_date 2025/10/18 · arxiv updated 2026/01/08 · openalex updated_date 2026/07/28

Abstract

Stochastic resonance (SR) manifests as switching dynamics between two quasi-stationary states in the stochastic Mackey-Glass equation. We identify chaotic SR, arising from the coexistence of resonance and chaos in stochastic dynamics. In contrast to classical SR, which is described by a random point attractor with a negative largest Lyapunov exponent, chaotic SR is described by a random strange attractor with a positive largest Lyapunov exponent. We observe chaotic SR in the Mackey-Glass equation as well as chaotic SR in the Duffing equation and the underdamped FitzHugh-Nagumo equation, demonstrating the universality of this phenomenon across a broad class of strongly nonlinear random dynamical systems.

Discussions

• Eiki Kojima, Yuzuru Sato: Resonance and chaos in the stochastic Mackey-Glass equation https://arxiv.org/abs/2505.04874 https://arxiv.org/pdf/2505.04874 https://arxiv.org/html/2505.04874 [bsky, 0 points, 1 comments]

Related

• Stochastic perturbation of integrable systems: a window to weakly chaotic systems
• Mechanism of stochastic resonance in viscoelastic channel flow
• A Relationship Between Parametric Resonance and Chaos
• Amplification of weak signals and stochastic resonance via on-off intermittency with symmetry breaking
• Stochastic resonance in a sinusoidal potential system: An analog simulation experiment