Spatio-temporal patterns of non-autonomous systems on hypergraphs: Turing and Benjamin–Feir mechanisms

Abstract

This paper examines the Turing patterns and the spatio-temporal chaos of non-autonomous systems defined on hypergraphs. The analytical conditions for Turing instability (TI) and Benjamin-Feir instability (BFI) are obtained by linear stability analysis using new comparison principles. The comparison with pairwise interactions is presented to reveal the effect of higher-order interactions on pattern formation. In addition, numerical simulations due to different non-autonomous mechanisms, such as time-varying diffusion coefficients, time-varying reaction kinetics and time-varying diffusion coupling are provided respectively, which verifies the efficiency of theoretical results.