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Chaotic stochastic resonance in Mackey-Glass equations
Eiki Kojima1, Yuzuru Sato2,3
1Department of Mathematics, Hokkaido University, N12 W7 Kita-ku, Sapporo 0600812, Hokkaido, Japan.
Chaos (Woodbury, N.Y.)
|March 25, 2026
Summary
We discovered chaotic stochastic resonance (SR), a new dynamic where resonance and chaos coexist. This phenomenon, observed in nonlinear systems, features a strange attractor unlike classical SR.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Statistical Physics
Background:
- Stochastic resonance (SR) typically involves switching dynamics between states.
- Classical SR is characterized by a random point attractor and a negative Lyapunov exponent.
Purpose of the Study:
- To identify and characterize a novel phenomenon termed chaotic stochastic resonance (chaotic SR).
- To demonstrate the universality of chaotic SR across different nonlinear systems.
Main Methods:
- Analysis of the stochastic Mackey-Glass equation.
- Investigation of chaotic dynamics using Lyapunov exponents.
- Observation of chaotic SR in Duffing and FitzHugh-Nagumo equations.
Main Results:
- Identification of chaotic SR, a state arising from the interplay of resonance and chaos.
- Chaotic SR is associated with a random strange attractor and a positive largest Lyapunov exponent.
- Chaotic SR was observed in multiple strongly nonlinear random dynamical systems.
Conclusions:
- Chaotic SR represents a new regime in stochastic dynamics.
- The phenomenon is not limited to a single system, indicating broad applicability.
- This finding expands the understanding of complex behaviors in nonlinear systems.
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