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Stochastic synchronization in nonlinear network systems driven by intrinsic and coupling noise.

Zahra Aminzare¹, Vaibhav Srivastava²

¹Department of Mathematics, University of Iowa, Iowa City, IA, USA. zahra-aminzare@uiowa.edu.

Biological Cybernetics

|April 20, 2022

Summary

This study examines how noise impacts synchronization in nonlinear systems. Common noise can hinder or help synchronization, while independent noise affects approximate synchronization in networks.

Keywords:

Approximate synchronization Heterogeneous networks Homogeneous networks Noisy networks Stochastic synchronization

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Area of Science:

Nonlinear dynamics
Network theory
Statistical physics

Background:

Networks of nonlinear systems are ubiquitous in science and engineering.
Understanding synchronization phenomena in these networks is crucial.
State-dependent noise, from intrinsic and coupling sources, complicates synchronization dynamics.

Purpose of the Study:

To investigate the influence of intrinsic and coupling noise on synchronization in nonlinear networks.
To differentiate the effects of common versus independent noise sources on network synchronization.
To provide numerical insights using coupled Van der Pol oscillators.

Main Methods:

Analysis of nonlinear systems subjected to state-dependent noise.
Mathematical modeling of intrinsic and coupling noise effects.
Numerical simulations to illustrate synchronization behaviors under different noise conditions.

Main Results:

Common noise can either enhance or impede network synchronization, depending on system parameters.
Independent noise primarily influences the degree of approximate synchronization within the network.
The coupled Van der Pol oscillator model demonstrates these noise-induced synchronization effects.

Conclusions:

Noise characteristics (common vs. independent) significantly alter synchronization patterns in nonlinear networks.
The interplay between intrinsic noise and coupling noise dictates overall network behavior.
Findings offer insights into controlling synchronization in complex noisy systems.