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

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. Published under an exclusive license by AIP Publishing.

Automated summary

Patched patterns, a new class of patterns in arrays of non-locally coupled excitable units with attractive and repulsive interactions, involve the formation of majority and minority patches characterized by uniform average spiking frequencies. Chaos typically emerges in patched patterns via torus breakup, with chaotic interfaces developing between units with average frequencies in between those of majority and minority patches. The maximal Lyapunov exponent of chaotic patched patterns converges to a finite value with system size, and patterns with smaller wavenumber may exhibit diffusive motion of chaotic interfaces similar to incoherent chimeras.