Delayed Feedback Control and Bifurcation Analysis of an Autonomy System | Zendy

Zhen Wang | Zendy; Huitao Zhao | Zendy; Xiangyu Kong | Zendy

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Delayed Feedback Control and Bifurcation Analysis of an Autonomy System

Author(s) -

Zhen Wang,

Huitao Zhao,

Xiangyu Kong

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/167065

Subject(s) - mathematics , hopf bifurcation , saddle node bifurcation , bogdanov–takens bifurcation , bifurcation , pitchfork bifurcation , bifurcation diagram , mathematical analysis , control theory (sociology) , chaotic , orbit (dynamics) , biological applications of bifurcation theory , transcritical bifurcation , zero (linguistics) , oscillation (cell signaling) , control (management) , nonlinear system , physics , quantum mechanics , artificial intelligence , computer science , engineering , aerospace engineering , linguistics , philosophy , management , biology , economics , genetics

An autonomy system with time-delayed feedback is studied by using the theory of functional differential equation and Hassard’s method; the conditions on which zero equilibrium exists and Hopf bifurcation occurs are given, the qualities of the Hopf bifurcation are also studied. Finally, several numerical simulations are given; which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable state or a stable periodic orbit

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