一类时滞微分系统的图灵—霍普夫分岔  

TURING-HOPF BIFURCATION OF A CLASS OF DELAY DIFFERENTIAL SYSTEMS

作　　者：任秀芳[1] 陈雅琪 梁永扬 朱闪闪 Ren Xiufang;Chen Yaqi;Liang Yongyang;Zhu Shanshan(Department of Mathematics,College of Science,Nanjing Agricultural University,Nanjing 210095)

机构地区：[1]南京农业大学理学院数学系,南京210095

出　　处：《南京大学学报（数学半年刊）》2020年第1期1-22,共22页Journal of Nanjing University(Mathematical Biquarterly)

基　　金：supported by fundamental research funds for the Central Universities Grants KJQN201717,KYZ201537;NSFC Grants 11601232,11775116;NSFC Grant 11601232;a Jiangsu provincial scholarship for overseas research;supported by the Scientific Research and Training program for College students Grant 1823A08 and NSFC Grant 11601232.

摘　　要：本文研究了一类具有有限时滞和扩散项的微分系统.我们分析了该系统解的稳定性,包括霍普夫分岔和图灵-霍普夫分岔.特别地,我们给出了用于描述时滞、两个扩散系数、波谱和波数的临界关系的一个清晰的公式,并且推导了与图灵-霍普夫分岔有关的波谱和波数的临界值.本文的结果基于中心流形定理、Hassard规范型理论和一些定量分析的技术.In this paper,we deal with a class of differential systems with finite time delay and diffusion terms.We analyze the stability of the solutions of this system,including the Hopf bifurcation and Turing-Hopf bifurcation.Particularly,we show a sharp formula depicting a threshold relationship among time delay,two diffusion coefficients,wave spectrum and wavenumber,and deduce the critical values of wave spectrum and wavenumber which relate to the Turing-Hopf bifurcation.The result is based on center manifold theorem,Hassard normal form theory and some qualitative analysis techniques.

关 键 词：图灵-霍普夫分岔 时滞 扩散 Hassard规范型 

分 类 号：O175.21[理学—数学]