An alternate mechanism for the emergence of localized oscillatory patterns in networked reaction-diffusion systems.

Abstract

Localized oscillatory patterns, confined to finite spatial domains or subsets of nodes in a network, have been observed in cortical neurons, metacommunity ecosystems, and chemical experiments.Previous studies have shown that wave bifurcations (oscillatory Turing instabilities) in undirected networked reaction-diffusion systems can induce such localized oscillations. Here, we propose an alternative mechanism for their emergence, namely Hopf-type instabilities acting on a subcritical Turing branch. Unlike wave bifurcations, this mechanism does not require interactions amongst at least three components. We further demonstrate its robustness in both the Brusselator and FitzHugh-Nagumo models in undirected Barabási-Albert, Erd˝os-Rényi, and Watts-Strogatz networks. This work extends the universality of such patterns in networked systems and provides a theoretical foundation for the control of collective dynamical phenomena in complex systems.