Breathing multichimera states in nonlocally coupled phase oscillators

Area of Science:

• Complex systems
• Nonlinear dynamics
• Network science

Background:

• Chimera states, a hybrid synchronization phenomenon, are typically studied as stationary states in nonlocally coupled oscillator networks.
• Previous research has hinted at the possibility of dynamic chimera states, specifically 'breathing' states, but their occurrence in multichimera systems remains less explored.

Purpose of the Study:

• To investigate the existence and characteristics of breathing multichimera states in a one-dimensional array of nonlocally coupled phase oscillators.
• To analyze the transition mechanism from stationary multichimera states to breathing ones.

Main Methods:

• Numerical simulations of the continuum limit of nonlocally coupled phase oscillators.
• Linear stability analysis applied to stationary multichimera states.

Main Results:

• Demonstration of the emergence of breathing multichimera states, featuring a temporally oscillating global order parameter.
• Identification of a Hopf bifurcation point where stationary multichimera states transition into breathing states.

Conclusions:

• Breathing multichimera states are a valid dynamical regime in these systems.
• Hopf bifurcation provides a theoretical framework for understanding the transition to dynamic chimera states.