Chaos control and Hopf bifurcation analysis of the Genesio system with distributed delays feedback

Advances in Difference Equations

Junbiao Guan¹  Guixiang Wang¹  Fangyue Chen¹ 

[1] School of Science, Hangzhou Dianzi University, Hangzhou, P.R. China

关键词: chaos control;    Hopf bifurcation;    distributed time delay;    feedback;   

DOI  :  10.1186/1687-1847-2012-166

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, the Genesio system with distributed time delay feedback is investigated. Firstly, the stability of the equilibria of the system is investigated by analyzing the characteristic equation, and then the existence of Hopf bifurcations is verified by choosing the mean time delay as a bifurcation parameter. Subsequent to that, the direction and stability of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. Finally, some numerical simulations are presented to verify the effectiveness of the theoretical results. MSC:34K10, 93D15.

【 授权许可】

CC BY