Pattern competition as a driver of diversity-induced resonance

Abstract

Diversity-induced resonance, the emergence of coherent spatiotemporal patterns at intermediate parameter disorder, is a well-known phenomenon in lattices of excitable elements. Here we study the pattern events behind diversity-induced resonance in a lattice of coupled FitzHugh-Nagumo oscillators. Starting out with the observation that maximal spiral wave counts occur at intermediate values of parameter diversity, we analyze the competition between spiral and target wave patterns in the asymptotic collective state. We devise stylized numerical “in silico” competition experiments of (individual) patterns to understand the regulating parameters of the competing pattern events occurring stochastically in the full (“in vivo”) numerical simulation. Our analysis shows that pattern competition is a principal driving mechanism behind this form of diversity-induced resonance and that different types of competition take place: some follow the frequency composition of target and spiral waves, others are dictated by the statistics of parameter distributions. In particular, the increase and decrease of spiral wave counts with increasing diversity are statistically regulated by the number of oscillatory elements in the lattice, rather than by the frequency differences between target and spiral waves.