延迟反馈对Turing和Hopf分岔转换的控制  

Control of delayed feedback over Turing and Hopf bifurcation transformations

作　　者：杨爽 马淑芳[1] YANG Shuang;MA Shufang(College of Science,Northeast Forestry University,Harbin 150040,China)

机构地区：[1]东北林业大学理学院,哈尔滨150040

出　　处：《哈尔滨商业大学学报（自然科学版）》2024年第5期585-591,共7页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：中央高校基本科研任务费(2572018BC19).

摘　　要：研究了一类反应扩散方程在延迟反馈控制下的时空不稳定性.将延迟视为扰动,分析了延迟对余维-2 Turing-Hopf相空间附近的Turing和Hopf不稳定性的影响.延迟显著地改变了振荡频率、本征波矢量以及Turing和Hopf模态的强度.可见适当的延迟可以控制Turing斑图和Hopf斑图之间的转换.结果表明,单个反馈或双反馈都可以实现Turing斑图与Hopf斑图之间转换的控制,从而说明了延迟反馈对控制余维-2 Turing-Hopf相空间附近的斑图形成方面的有效性.This paper studied on the spatiotemporal instability of a class of reaction-diffusion equations under delayed feedback control.In this paper,the impact of delay on Turing and Hopf instability in the vicinity of codimension-2 Turing-Hopf phase space was analyzed,where the time delay was treated as a perturbation.It was found that the presence of delay significantly altered the oscillation frequency,the intrinsic wave vector,and the intensities of both Turing and Hopf modes,which mean that the application of appropriate time delay can modulate the competition between the Turing and Hopf modes.Furthermore,the analysis showed that either single feedback or double feedback can control the transformation between Turing and Hopf patterns,demonstrating the effectiveness of delayed feedback in controlling the formation of patterns near codimension-2 Turing-Hopf phase space.

关 键 词：斑图形成 反应扩散系统 延迟反馈 稳定性 Turing斑图 Hopf斑图 

分 类 号：O175.21[理学—数学]