Paper Info
Title
Delay Feedback Control For Interaction Of Hopf And Period Doubling Bifurcations In Discrete-Time Systems
Abstract
Interaction of Hopf and period doubling bifurcations, as a so-called codimension two singularity, may give rise to rich bifurcation outcomes depending on the two-parameter unfolding at the bifurcation point. In this paper, we develop a nonlinear delay control for interaction of Hopf and period doubling bifurcations at a desired parameter location with preferred bifurcation properties. For its linear control term, the gains are determined by the bifurcation critical conditions and are used to create this type of bifurcations at a desired parameter location. For its nonlinear control term, the gains are derived by the center manifold theorem and theory of normal form. They determine the type and stability of bifurcation solutions. The proposed control method is applicable to any uncontrolled system which can be stable, unstable or even chaotic. Numerical experiments verify the feasibility of the control methodology and clearly show easy manipulation of all kinds of possible solutions of the created bifurcation.
Year
DOI
Venue
2006
10.1142/S0218127406014617
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Keywords
DocType
Volume
bifurcation control, interaction of Hopf and period doubling bifurcations, Hopf-flip bifurcation, delay feedback, discrete-tirne system
Journal
16
Issue
ISSN
Citations 
1
0218-1274
1
PageRank 
References 
Authors
0.51
5
3
Name
Order
Citations
PageRank
Guilin Wen17610.24
Qing-guo Wang210.51
Min-sen Chiu3174.96