Paper Info
Title
On Stability Switches and Bifurcation of the Modified Autonomous Van der Pol-Duffing Equations via Delayed State Feedback Control
Abstract
This paper considers the Modified Autonomous Van der Pol-Duffing equation subjected to dynamic state feedback, which can well characterize the dynamic behaviors of the nonlinear dynamical systems. Both the issues of local stability switches and the Hopf bifurcation versus time delay are investigated. Associating with the tau decomposition strategy and the center manifold theory, the delay stable intervals and the direction and stability of the Hopf bifurcation are all determined. Specifically, the computation of purely imaginary roots (symmetry to the real axis), the positive real root formula for cubic equation and the sophisticated bilinear form of adjoint operators are proposed, which make the calculations mentioned in our discussion unified and simple. Finally, the typical numerical examples are shown to illustrate the correctness and effectiveness of the practical technique.
Year
DOI
Venue
2021
10.3390/sym13122336
SYMMETRY-BASEL
Keywords
DocType
Volume
stability switches, Hopf bifurcation, tau-decomposition method, center manifold theory
Journal
13
Issue
Citations 
PageRank 
12
0
0.34
References 
Authors
0
4
Name
Order
Citations
PageRank
Tiao Yang Cai100.34
Hui-Long Jin200.68
Hong Yu300.68
Xiang-Peng Xie400.34