# Chimera dynamics in nonlocally coupled moving phase oscillators

## TL;DR

This paper investigates how agent mobility influences chimera states in nonlocally coupled phase oscillators, revealing mobility-dependent transitions, stochastic jumping among states, and scaling laws in dynamical regimes.

## Contribution

It introduces a dynamic interaction structure with agent movement affecting chimera states, extending understanding beyond static interaction models.

## Key findings

- Mobility causes transitions between dynamical states depending on phase lag.
- Agents exhibit stochastic jumps among states at intermediate mobility.
- Scaling laws relate transient times and state lifetimes to mobility.

## Abstract

Chimera states, a symmetry-breaking spatiotemporal pattern in nonlocally coupled dynamical units, prevail in a variety of systems. However, the interaction structures among oscillators are static in most of studies on chimera state. In this work, we consider a population of agents. Each agent carries a phase oscillator. We assume that agents perform Brownian motions on a ring and interact with each other with a kernel function dependent on the distance between them. When agents are motionless, the model allows for several dynamical states including two different chimera states (the type-I and the type-II chimeras). The movement of agents changes the relative positions among them and produces perpetual noise to impact on the model dynamics. We find that the response of the coupled phase oscillators to the movement of agents depends on both the phase lag $\alpha$, determining the stabilities of chimera states, and the agent mobility $D$. For low mobility, the synchronous state transits to the type-I chimera state for $\alpha$ close to $\pi/2$ and attracts other initial states otherwise. For intermediate mobility, the coupled oscillators randomly jump among different dynamical states and the jump dynamics depends on $\alpha$. We investigate the statistical properties in these different dynamical regimes and present the scaling laws between the transient time and the mobility for low mobility and relations between the mean lifetimes of different dynamical states and the mobility for intermediate mobility.