Propensity criterion for networking in an array of coupled chaotic systems

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Network Science

Background:

• Mutual synchronization is crucial for emergent behavior in coupled chaotic systems.
• Understanding how local chaos and stability interact is key to network function.
• Previous research has explored chaos in lasers and single neurons.

Purpose of the Study:

• To introduce a criterion for network propensity based on attractor properties.
• To investigate the emergence of global behavior from local chaotic elements.
• To compare homoclinic chaos with Lorenz chaos using this criterion.

Main Methods:

• Characterizing individual chaotic elements in a one-dimensional chain.
• Analyzing the emergence of global nontrivial behavior.
• Introducing and applying a propensity criterion for networking.
• Comparing homoclinic and Lorenz chaotic attractors.

Main Results:

• A propensity criterion for networking is defined by the coexistence of a sensitive chaotic region and a stable coupling island within the attractor.
• This criterion facilitates the emergence of global nontrivial behavior from local chaotic elements.
• Homoclinic chaos and Lorenz chaos are compared based on their suitability for network synchronization.

Conclusions:

• The proposed propensity criterion effectively predicts network synchronization capabilities.
• The interplay between localized chaos and stable coupling is essential for reliable network function.
• The findings offer insights into synchronization mechanisms in systems like coupled neurons.