Study on Spatiotemporal Pattern Evolution Mechanism of Schnakenberg System
Schnakenberg system is a typical chemical reaction-diffusion control system.Currently,research both do-mestically and internationally is limited to Turing instability and bifurcation of such system,with relatively fewer reports on the evolution mechanism of its chemical patterns.Pattern mechanism analysis can accurately reveal the generation of self-organization phenomena and the evolution of spatial patterns in chemical reactions.This paper in-vestigates the structural transformation,evolution speed,and time-dependence of patterns of Schnakenberg system under cross-diffusion driving,and focuses on exploring the response mechanism of cross-diffusion to its kinetics and pattern evolution.The findings indicate that when a system induced by self-diffusion is stable,cross-diffusion can trigger pattern formation.When a system induced by self-diffusion is unstable,cross-diffusion can lead to the trans-formation of pattern structures.For circular wave structures,different components of cross-diffusion can influence their evolution speed.In the context of temporal dependence,cross-diffusion can trigger the generation of patterns that vary periodically with time and can transform such patterns into relatively stable ones over time.Therefore,cross-diffusion plays a crucial role in the pattern generation,transformation,evolution speed,and temporal depend-ence of Schnakenberg system.
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