Synchronization of noisy systems by stochastic signals

Area of Science:

• Nonlinear dynamics
• Stochastic processes
• Statistical physics

Background:

• Bistable systems exhibit complex dynamics under external stimuli.
• Understanding synchronization in noisy systems is crucial for various scientific fields.
• Markovian dichotomic noise presents a unique challenge for system analysis.

Purpose of the Study:

• To analyze the synchronization phenomena in noisy bistable systems subjected to stochastic signals.
• To develop a general kinetic model for analytically studying nonlinear responses.
• To investigate the role of dichotomic noise in system synchronization and its relation to stochastic resonance.

Main Methods:

• Development of a general kinetic model for analytical treatment.
• Calculation of cross-correlation measures and mean switching frequency.
• Numerical simulations of a noisy overdamped bistable oscillator.
• Comparison of theoretical predictions with simulation results.

Main Results:

• Dichotomic noise can instantaneously synchronize the switching process in bistable systems.
• Synchronization is most pronounced at an optimal noise intensity, demonstrating a link to aperiodic stochastic resonance.
• Similar synchronization effects were observed in a stochastic neuron model driven by stochastic spike trains.

Conclusions:

• Dichotomic noise offers a mechanism for controlling and enhancing synchronization in noisy nonlinear systems.
• The findings provide insights into the interplay between noise, nonlinearity, and synchronization, with implications for signal processing and biological systems.
• The study highlights the potential of stochastic resonance-like phenomena in noise-induced synchronization.