Oscillation death in coupled counter-rotating identical nonlinear oscillators.

Area of Science:

• Nonlinear dynamics
• Complex systems
• Theoretical physics

Background:

• Coupled nonlinear oscillators exhibit diverse dynamical behaviors.
• Understanding oscillation suppression is crucial for complex system analysis.
• Previous studies have identified limit cycles and amplitude death.

Purpose of the Study:

• To investigate oscillatory and oscillation-suppressed phases in coupled counter-rotating nonlinear oscillators.
• To clarify bifurcations between different dynamical states.
• To introduce and characterize a new type of oscillation suppression: oscillation death.

Main Methods:

• Analysis of coupled counter-rotating nonlinear oscillator models.
• Identification and characterization of limit cycle, amplitude death, and oscillation death states.
• Investigation of Hopf, pitchfork, and infinite period bifurcations.
• Exploration of neutral stability in non-conservative systems using anti-parity-time symmetry and exceptional points in non-Hermitian systems.

Main Results:

• Demonstrated the existence of limit cycle, amplitude death, and oscillation death.
• Clarified the bifurcations (Hopf, pitchfork, infinite period) governing transitions between these states.
• Identified oscillation death as a novel oscillation suppression characterized by neutrally stable inhomogeneous steady states.
• Showcased the robust neutral stability of oscillation death in non-conservative systems via anti-parity-time-symmetric phase transitions at exceptional points.

Conclusions:

• Oscillation death represents a new and robust form of oscillation suppression in nonlinear systems.
• Anti-parity-time symmetry and exceptional points offer a framework for understanding oscillation death in non-Hermitian and non-conservative systems.
• The study clarifies fundamental bifurcations in coupled oscillator dynamics.