Spatiotemporal patterns in coupled reaction-diffusion systems with nonidentical kinetics

Understanding of the effect of coupling interaction is at the heart of nonlinear science since some nonequilibrium systems are composed of different layers or units. In this paper, we demonstrate various spatio-temporal patterns in a nonlinearly coupled two-layer Turing system with nonidentical reaction kinetics. Both the type of Turing mode and coupling form play an important role in the pattern formation and pattern selection. Two kinds of Turing mode interactions, namely supercritical-subcritical and supercritical-supercritical Turing mode interaction, have been investigated. Stationary resonant superlattice patterns arise spontaneously in both cases, while dynamic patterns can also be formed in the latter case. The destabilization of spike solutions induced by spatial heterogeneity may be responsible for these dynamic patterns. In contrast to linear coupling, the nonlinear coupling not only increases the complexity of spatio-temporal patterns, but also reduces the requirements of spatial resonance conditions. The simulation results are in good agreement with the experimental observations in dielectric barrier discharge systems.