# Chimeras and clusters in networks of hyperbolic chaotic oscillators

## TL;DR

This paper demonstrates the emergence of chimera states in networks of hyperbolic chaotic oscillators, specifically Lozi maps, revealing that hyperbolicity does not prevent chimera formation and characterizing their collective behavior.

## Contribution

It shows that chimera states can form in hyperbolic chaotic oscillator networks, challenging previous assumptions about hyperbolicity's role in such phenomena.

## Key findings

- Chimera states coexist with clusters and incoherence.
- Chimera states occur in nonlocally coupled networks with long-range interactions.
- Hyperbolicity does not prevent chimera formation in chaotic networks.

## Abstract

We show that chimera states, where differentiated subsets of synchronized and desynchronized dynamical elements coexist, can emerge in networks of hyperbolic chaotic oscillators subject to global interactions. As local dynamics we employ Lozi maps which possess hyperbolic chaotic attractors. We consider a globally coupled system of these maps and use two statistical quantities to describe its collective behavior: the average fraction of elements belonging to clusters and the average standard deviation of state variables. Chimera states, clusters, complete synchronization, and incoherence are thus characterized on the space of parameters of the system. We find that chimera states are related to the formation of clusters in the system. In addition, we show that chimera states arise for a sufficiently long range of interactions in nonlocally coupled networks of these maps. Our results reveal that, under some circumstances, hyperbolicity does not impede the formation of chimera states in networks of coupled chaotic systems, as it had been previously hypothesized.