Schnakenberg系统的时空斑图演化机理研究OA北大核心CSTPCD
Study on Spatiotemporal Pattern Evolution Mechanism of Schnakenberg System
Schnakenberg系统是一类典型的化学反应扩散控制系统.目前国内外研究仅局限于Schnakenberg系统的Tur-ing 不稳定与分岔,而关于其化学斑图演化机理的报道较少.斑图机理分析可以准确揭示化学反应中自组织现象的产生和空间模式的演化规律.本文研究交叉扩散驱动下Schnakenberg系统斑图的结构蜕变、演化速度及时间依赖性,重点探讨交叉扩散对其动力学与斑图演化的响应机制.研究发现,当自扩散诱导的系统稳定时,交叉扩散可以激发斑图的产生;当自扩散诱导的系统不稳定时,交叉扩散可以实现斑图结构的蜕变;对于环波结构,不同组分的交叉扩散可以影响其演化速度;对于时间依赖性,交叉扩散可以激发随时间周期变化的斑图产生,并可将此类斑图转换为随时间相对稳定的斑图.因此,交叉扩散对于Schnakenberg系统的斑图产生、蜕变、演化速度及时间依赖性都起着至关重要的作用.
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.
董顺科;肖敏;虞文武
南京邮电大学自动化学院、人工智能学院 南京 210023东南大学数学学院 南京 211189
交叉扩散Schnakenberg系统时空斑图稳定性环波
Cross-diffusionSchnakenberg systemspatiotemporal patternsstabilitycircular wave
《自动化学报》 2024 (008)
1620-1630 / 11
国家自然科学基金(62073172,62233004,62073076),江苏省自然科学基金(BK20221329),江苏省应用数学科学研究中心(BK20233002)资助Supported by National Natural Science Foundation of China(62073172,62233004,62073076),Natural Science Foundation of Jiangsu Province of China(BK20221329),and Jiangsu Provin-cial Scientific Research Center of Applied Mathematics(BK20233002)
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