Noise-induced coherence in bistable systems with multiple time delays

Area of Science:

• Nonlinear dynamics
• Stochastic processes
• Complex systems

Background:

• Bistable systems are fundamental in various scientific fields.
• Time-delay feedback significantly influences system dynamics.
• Understanding correlation properties is crucial for characterizing system behavior.

Purpose of the Study:

• To investigate the correlation properties of noise-driven bistable systems with multiple time-delay feedbacks.
• To analyze the impact of single versus double time delays on system dynamics.
• To derive and compare autocorrelation functions and power spectra.

Main Methods:

• Utilized a two-state model for noise-driven bistable systems.
• Incorporated transition rates dependent on earlier system states.
• Derived analytical expressions for autocorrelation function and power spectrum.
• Performed comparative analysis for single and double time delays.

Main Results:

• Derived autocorrelation function and power spectrum for small perturbations and feedback.
• Observed exponential decay with minor undulations in autocorrelation for double time delays.
• Contrasted this with remarkable oscillatory behavior at small time lags for single time delays.

Conclusions:

• Multiple time delays qualitatively alter the correlation properties of bistable systems.
• Double time delays lead to smoother correlation decay compared to single time delays.
• The findings offer insights into the control of noise-induced phenomena in dynamical systems.