Chaotic stochastic resonance in Mackey-Glass equations

TL;DR

This paper introduces chaotic stochastic resonance in nonlinear stochastic systems, showing it as a universal phenomenon characterized by coexistence of resonance and chaos, with positive Lyapunov exponents.

Contribution

It identifies and characterizes chaotic stochastic resonance in the Mackey-Glass equation and demonstrates its universality across various nonlinear systems.

Findings

Chaotic SR occurs with positive Lyapunov exponents.

Chaotic SR observed in Mackey-Glass, Duffing, and FitzHugh-Nagumo equations.

Chaotic SR differs from classical SR by involving chaos and strange attractors.

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.