Simple estimation of synchronization threshold in ensembles of diffusively coupled chaotic systems

Area of Science:

• Nonlinear Dynamics
• Chaos Theory
• Complex Systems

Background:

• Coupled chaotic systems are fundamental in understanding complex phenomena.
• Predicting chaotic synchronization is crucial for many applications.
• Existing methods for synchronization analysis can be complex and system-specific.

Purpose of the Study:

• To define a simple and universally applicable criterion for the synchronization threshold in coupled chaotic systems.
• To identify the key parameters governing chaotic synchronization.
• To provide a method applicable to diverse network topologies.

Main Methods:

• Development of a synchronization criterion based on linear analysis of dynamical systems.
• Identification of two key parameters of order: the largest Lyapunov exponent and the coupling coefficient.
• Application to ensembles of simplest dynamical systems for stability analysis.

Main Results:

• A simple criterion for chaotic synchronization threshold is defined.
• Synchronization is shown to depend only on the largest Lyapunov exponent and coupling coefficient.
• The criterion is applicable to regular and irregular network structures.

Conclusions:

• The proposed criterion offers a simplified approach to understanding chaotic synchronization.
• The findings are robust across different network configurations.
• Numerical simulations validate the high precision of the linear analysis approach.