Patched patterns and emergence of chaotic interfaces in arrays of nonlocally coupled excitable systems

TL;DR

This paper introduces patched patterns in nonlocally coupled excitable systems, revealing how chaos and interfaces emerge through bifurcations, with implications for understanding complex spatiotemporal behaviors.

Contribution

It uncovers a new class of patterns called patched patterns, detailing their formation, chaotic dynamics, and bifurcation mechanisms in coupled excitable units.

Findings

Chaotic patterns emerge via torus breakup.

Chaotic interface bifurcations are identified.

Lyapunov exponent converges with system size.

Abstract

We disclose a new class of patterns, called patched patterns, in arrays of non-locally coupled excitable units with attractive and repulsive interactions. Self-organization process involves formation of two types of patches, majority and minority ones, characterized by uniform average spiking frequencies. Patched patterns may be temporally periodic, quasiperiodic or chaotic, whereby chaotic patterns may further develop interfaces comprised of units with average frequencies in between those of majority and minority patches. Using chaos and bifurcation theory, we demonstrate that chaos typically emerges via a torus breakup and identify the secondary bifurcation that gives rise to chaotic interfaces. It is shown that the maximal Lyapunov exponent of chaotic patched patterns does not decay, but rather converges to a finite value with system size. Patched patterns with a smaller wavenumber may exhibit diffusive motion of chaotic interfaces, similar to that of the incoherent part of chimeras.