Emerging chimera states under nonidentical counter-rotating oscillators

Area of Science:

• Nonlinear dynamics
• Complex systems
• Network science

Background:

• Collective dynamics in coupled oscillator systems are crucial for understanding complex phenomena.
• Frequency and perturbation significantly influence system behavior and emergent states.
• Parity (P) symmetry plays a role in the dynamics of coupled oscillators.

Purpose of the Study:

• Investigate the impact of counter-rotating frequencies on dynamical transitions in coupled Stuart-Landau oscillators.
• Analyze the emergence and properties of chimera states under perturbation.
• Quantify and understand the role of parity symmetry in different dynamical states.

Main Methods:

• Numerical simulations of globally coupled nonidentical Stuart-Landau oscillators.
• Analysis of dynamical transitions, including partial synchronization, amplitude death, and oscillation death.
• Basin stability analysis to investigate symmetry-breaking phenomena.
• Development of a measure to quantify parity symmetry strength.

Main Results:

• In the absence of perturbation, systems transition through partial synchronization to death states, with observed states lacking P symmetry.
• Perturbation induces transitions from incoherent to coherent mixed synchronization via chimera states.
• Chimera states exhibit partial P symmetry breaking, arising from coexisting symmetry-preserving and breaking behaviors.
• The chimera state is robust to network size increases and observed in other oscillator models.

Conclusions:

• Counter-rotating frequencies and perturbation are key drivers of complex dynamics and symmetry breaking in coupled oscillator networks.
• Chimera states represent a significant finding, demonstrating partial symmetry breaking.
• The study provides a framework for quantifying P symmetry and understanding its role in complex systems.