Bifurcation analysis and control of periodic solutions changing into invariant tori in Langford system
Liu Su-Hua(刘素华)a)b)† , Tang Jia-Shi(唐驾时)a), Qin Jin-Qi(秦金旗)a), and Yin Xiao-Bo(尹小波)c)
a College of Mechanics and Aerospace, Hunan University, Changsha 410082, China; b Anyang Institute of Technology, Anyang 455000, China; c School of Geoscience and Environmental Engineering, Central South University, Changsha 410083, China
Abstract Bifurcation characteristics of the Langford system in a general form are systematically analysed, and nonlinear controls of periodic solutions changing into invariant tori in this system are achieved. Analytical relationship between control gain and bifurcation parameter is obtained. Bifurcation diagrams are drawn, showing the results of control for secondary Hopf bifurcation and sequences of bifurcations route to chaos. Numerical simulations of quasi-periodic tori validate analytic predictions.
Received: 26 July 2007
Revised: 29 November 2007
Accepted manuscript online:
Fund: Project
supported by the National Natural Science Foundation of
China (Grant No 10672053).
Cite this article:
Liu Su-Hua(刘素华), Tang Jia-Shi(唐驾时), Qin Jin-Qi(秦金旗), and Yin Xiao-Bo(尹小波) Bifurcation analysis and control of periodic solutions changing into invariant tori in Langford system 2008 Chin. Phys. B 17 1691
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