# A model bridging chimera state and explosive synchronization

## TL;DR

This paper introduces a new model that connects chimera states and explosive synchronization in coupled oscillators, revealing conditions under which each phenomenon occurs and how they can coexist.

## Contribution

The study presents a novel adaptive coupling model that bridges chimera states and explosive synchronization, providing insights into their relationship and initial condition dependence.

## Key findings

- Model exhibits CS or ES in two limits
- Both CS and ES can coexist in intermediate regimes
- Initial conditions influence basin patterns of CS

## Abstract

Global and partial synchronization are the two distinctive forms of synchronization in coupled oscillators and have been well studied in the past decades. Recent attention on synchronization is focused on the chimera state (CS) and explosive synchronization (ES), but little attention has been paid to their relationship. We here study this topic by presenting a model to bridge these two phenomena, which consists of two groups of coupled oscillators and its coupling strength is adaptively controlled by a local order parameter. We find that this model displays either CS or ES in two limits. In between the two limits, this model exhibits both CS and ES, where CS can be observed for a fixed coupling strength and ES appears when the coupling is increased adiabatically. Moreover, we show both theoretically and numerically that there are a variety of CS basin patterns for the case of identical oscillators, depending on the distributions of both the initial order parameters and the initial average phases. This model suggests a way to easily observe CS, in contrast to others models having some (weak or strong) dependence on initial conditions.