Oscillation death in coupled counter-rotating identical nonlinear oscillators

Abstract

We study oscillatory and oscillation suppressed phases in coupled counter-rotating nonlinear oscillators. We demonstrate the existence of limit cycle, amplitude death, and oscillation death, and also clarify the Hopf, pitchfork, and infinite period bifurcations between them. Especially, the oscillation death is a new type of oscillation suppressions of which the inhomogeneous steady states are neutrally stable. We discuss the robust neutral stability of the oscillation death in non-conservative systems via the anti-PT-symmetric phase transitions at exceptional points in terms of non-Hermitian systems.

7 pages, 4 figures

References in corpus (6)

• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
• Distributed Delays Facilitate Amplitude Death of Coupled Oscillators
• Gain-Driven Discrete Breathers in PT-Symmetric Nonlinear Metamaterials
• Systems of coupled PT-symmetric oscillators
• Exceptional points in coupled dissipative dynamical systems

Cited by in corpus (2)

• Anti-$\mathcal{P}\mathcal{T}$-symmetric Kerr gyroscope
• Dynamics in non-Hermitian systems with nonreciprocal coupling