# Oscillation death in coupled counter-rotating identical nonlinear oscillators

## TL;DR

This paper investigates various oscillation suppression phenomena in coupled counter-rotating nonlinear oscillators, revealing new insights into oscillation death and its stability through bifurcation analysis and non-Hermitian system concepts.

## Contribution

It introduces the concept of oscillation death as a neutrally stable inhomogeneous steady state and links it to anti-PT-symmetric phase transitions in non-Hermitian systems.

## Key findings

- Identification of limit cycle, amplitude death, and oscillation death regimes.
- Clarification of bifurcation types leading to oscillation suppression.
- Demonstration of neutral stability of oscillation death linked to anti-PT symmetry.

## 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.