Chimera states in networks of logistic maps with hierarchical connectivities

TL;DR

This paper investigates how hierarchical and fractal connectivities in networks of logistic maps influence the emergence and complexity of chimera states, revealing that network structure significantly affects pattern formation.

Contribution

It systematically analyzes the impact of hierarchical network connectivities on chimera states, highlighting the role of clustering and symmetry in their formation.

Findings

High clustering coefficient promotes chimera states

Asymmetric connectivities lead to nested chimera patterns

Hierarchical level influences pattern complexity

Abstract

Chimera states are complex spatiotemporal patterns consisting of coexisting domains of coherence and incoherence. We study networks of nonlocally coupled logistic maps and analyze systematically how the dilution of the network links influences the appearance of chimera patterns. The network connectivities are constructed using an iterative Cantor algorithm to generate fractal (hierarchical) connectivities. Increasing the hierarchical level of iteration, we compare the resulting spatiotemporal patterns. We demonstrate that a high clustering coefficient and symmetry of the base pattern promotes chimera states, and asymmetric connectivities result in complex nested chimera patterns.