科研之友
微信
新浪微博
Facebook
分享链接
摘要
We study the Hopf bifurcation of C-3 differential systems in R-n showing that l limit cycles can bifurcate from one singularity with eigenvalues /- bi and n - 2 zeros with l is an element of {0, 1, ..., 2(n-3)}. As far as we know this is the first time that it is proved that the number of limit cycles that can bifurcate in a Hopf bifurcation increases exponentially with the dimension of the space. To prove this result, we use first-order averaging theory. Further, in dimension 4 we characterize the shape and the kind of stability of the bifurcated limit cycles. We apply our results to certain fourth-order differential equations and then to a simplified Marchuk model that describes immune response.
- 出版日期2009-4
- 单位上海交通大学
