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Self-emerging and turbulent chimeras in oscillator chains.
Grigory Bordyugov1, Arkady Pikovsky, Michael Rosenblum
1Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Straße 24/25, 14476 Potsdam, Germany. grigory.bordyugov@uni-potsdam.de
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
Summary
A novel chimera state, featuring coexisting synchrony and desynchrony, self-emerges in coupled oscillators. This phenomenon arises from a homogeneous state and can transition to phase turbulence.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Network science
Background:
- Chimera states represent a unique phenomenon in coupled oscillator systems, characterized by coexisting regions of synchronized and desynchronized behavior.
- Understanding the emergence and dynamics of chimera states is crucial for comprehending complex systems with interacting components.
Purpose of the Study:
- To report the self-emergence of a chimera state in a homogeneous chain of nonlocally and nonlinearly coupled oscillators.
- To develop a theoretical framework for understanding this emergent chimera state.
- To investigate the stability of the chimera state and its transition to other dynamical regimes.
Main Methods:
- The study utilizes a homogeneous chain of nonlocally and nonlinearly coupled oscillators.
- A theory for the chimera state is developed based on the Ott-Antonsen equations for the complex order parameter.
- Numerical linear stability analysis is employed to study the system's dynamics.
Main Results:
- A chimera state, defined by coexisting regions of complete and partial synchrony, self-emerges via a supercritical bifurcation from a homogeneous state.
- The developed theory successfully describes the emergence and characteristics of the chimera state.
- Instability analysis reveals a transition from the chimera state to phase turbulence, characterized by persistent patches of synchrony.
Conclusions:
- The study demonstrates the spontaneous emergence of chimera states in a specific oscillator network configuration.
- The theoretical framework provides valuable insights into the underlying mechanisms of chimera formation.
- The findings highlight the complex dynamics that can arise in coupled systems, including transitions to turbulent behavior.
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