Self-induced switchings between multiple space-time patterns on complex networks of excitable units

Abstract

We report on self-induced switchings between multiple distinct space--time patterns in the dynamics of a spatially extended excitable system. These switchings between low-amplitude oscillations, nonlinear waves, and extreme events strongly resemble a random process, although the system is deterministic. We show that a chaotic saddle -- which contains all the patterns as well as channel-like structures that mediate the transitions between them -- is the backbone of such a pattern switching dynamics. Our analyses indicate that essential ingredients for the observed phenomena are that the system behaves like an inhomogeneous oscillatory medium that is capable of self-generating spatially localized excitations and that is dominated by short-range connections but also features long-range connections. With our findings, we present an alternative to the well-known ways to obtain self-induced pattern switching, namely noise-induced attractor hopping, heteroclinic orbits, and adaptation to an external signal. This alternative way can be expected to improve our understanding of pattern switchings in spatially extended natural dynamical systems like the brain and the heart.