Spatial Pattern Switching Strategy: A Successful Application in the Bimolecular Model

Abstract

The formation of spatial patterns plays a crucial role in the study of system spatiotemporal dynamics. Previous research has demonstrated that spatial patterns can effectively characterize the macroscopic spatial structure of the reaction-diffusion system. While specific pattern structures, such as the hexagonal, mixed, and stripe pattern, have been identified, the interconnection between these patterns appears to be isolated and invariant. To facilitate the selection and switching between individual spatial patterns, the hybrid control strategy is applied to the bimolecular model for the first time. For the classical bimolecular model of the chemical reaction-diffusion system, the incorporation of two-dimensional diffusion extends its reaction space to the two-dimensional plane. The Turing instability conditions are obtained for the controlled bimolecular system. Through the weakly nonlinear analysis, the amplitude equations are derived near the Turing bifurcation threshold. Furthermore, we investigate the impact of each control parameter on the Turing bifurcation threshold and determine the distribution of spatial patterns and their stability through the amplitude equations. Simulation results indicate that by selecting appropriate control parameters, we can suppress the occurrence of Turing instability and facilitate transitions between the spatial patterns. The findings of the analysis offer valuable insights into the dynamics and control of pattern formation in reaction-diffusion systems.