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Chaotic stochastic resonance in Mackey-Glass equations.

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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.

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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.