Asymmetric cluster and chimera dynamics in globally coupled systems

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Spatiotemporal Systems

Background:

• Investigating emergent phenomena in coupled dynamical systems.
• Understanding asymmetric dynamics in subpopulations is crucial.
• Chimera and cluster states present unique synchronization patterns.

Purpose of the Study:

• To explore asymmetric chimera and cluster states in globally coupled systems.
• To elucidate the mechanisms behind these asymmetric dynamics.
• To establish predictive conditions for their formation.

Main Methods:

• Utilizing a network of globally coupled chaotic maps.
• Employing an analogy between driven maps and coupled map systems.
• Analyzing dynamical responses of driven maps.

Main Results:

• Identified asymmetric chimera states with stationary/periodic vs. chaotic dynamics.
• Characterized asymmetric cluster states with differing trajectory periods.
• Established a condition for dynamical equivalence between driven and coupled maps.

Conclusions:

• The derived condition predicts parameter values and partitions for asymmetric states.
• This work provides a framework for understanding and generating asymmetric dynamics.
• The findings are applicable to various spatiotemporal systems exhibiting complex behaviors.