Robustness of chimera states in complex dynamical systems

Area of Science:

• Complex systems
• Nonlinear dynamics
• Network science

Background:

• Chimera states, where identical oscillators display distinct behaviors, are a key phenomenon in non-locally coupled systems.
• Understanding the robustness of chimera states against network perturbations is crucial for theoretical and experimental validation.

Purpose of the Study:

• To investigate the impact of random link removal on the probability of chimera states in coupled oscillator systems.
• To determine how network structure perturbations affect the stability and occurrence of chimera states.

Main Methods:

• Direct numerical calculations were employed to simulate systems with random link removal.
• Two independent theoretical approaches were utilized to analyze the probability of chimera states.

Main Results:

• The probability of observing chimera states significantly decreases as the rate of random link removal increases.
• Even with substantial link removal, distinct coherent and incoherent regions persist in the state space.
• The chimera state emerges as a specific condition where oscillators in the coherent region achieve synchronization or phase-locking.

Conclusions:

• Chimera states are sensitive to random perturbations in network connectivity.
• The underlying network structure retains organized regions (coherent and incoherent) even when chimera states are suppressed.
• Further research can explore the conditions under which partial synchronization within coherent regions defines the chimera state regime.