南京理工大学学报（自然科学版）2025，Vol.49Issue(5)：612-624,13.DOI:10.14177/j.cnki.32-1397n.2025.49.05.010
基于状态反馈控制策略的交叉扩散Sel'kov-Schnakenberg系统时空动力学研究
Spatiotemporal dynamics in the cross-diffusion Sel'kov-Schnakenberg system based on a state feedback control strategy
摘要
Abstract
Pattern dynamics and control are forefront topics in both natural and engineering fields.To address the limitation of traditional Sel'kov-Schnakenberg models that consider only self-diffusion,this study incorporates cross-diffusion mechanisms to construct a novel Sel'kov-Schnakenberg system and designs a state feedback control strategy to optimize pattern dynamics.Firstly,the effect of the cross-diffusion coefficient as a bifurcation parameter on system stability and pattern structure is explored.Subsequently,the role of the state feedback controller in the spatiotemporal dynamics of the system is analyzed in depth.Numerical simulations reveal that while self-diffusion maintains system stability,cross-diffusion effectively triggers Turing pattern self-organization.When self-diffusion induces Turing instability,cross-diffusion drives significant phase transitions in pattern morphology.Furthermore,adjusting the state feedback controller gain kp from-0.5 to 0.5 shifts the Turing bifurcation threshold from-0.070 1 to 0.041 8.This study confirms that cross-diffusion mechanisms more accurately characterize coupled diffusion effects between substances,while feedback control provides an effective technical pathway for optimizing pattern dynamics.关键词
交叉扩散/Sel'kov-Schnakenberg模型/状态反馈控制/Turing失稳/斑图模式Key words
cross-diffusion/Sel'kov-Schnakenberg model/state feedback control/Turing instability/pattern formation分类
数学引用本文复制引用
李佳旺,肖敏,周映江,徐丰羽..基于状态反馈控制策略的交叉扩散Sel'kov-Schnakenberg系统时空动力学研究[J].南京理工大学学报（自然科学版）,2025,49(5):612-624,13.基金项目
国家自然科学基金(62073172) （62073172）
江苏省自然科学基金(BK20221329) （BK20221329）
