Patched patterns and emergence of chaotic interfaces in arrays of nonlocally coupled excitable systems
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Date
2022-09-16
Authors
Journal Title
Journal ISSN
Volume Title
Journal Title
Chaos: An Interdisciplinary Journal of Nonlinear Science
Volume Title
32
Article Title
091102
Publisher
AIP Publishing
Abstract
We disclose a new class of patterns, called patched patterns, in arrays of non-locally coupled excitable units with attractive and repulsive interactions. The self-organization process involves the 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.