Bifurcation control for a non-autonomous system with two time delays | Zendy

Qian Chang-zhao | Zendy; Tang Jia-Shi | Zendy

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Bifurcation control for a non-autonomous system with two time delays

Author(s) -

Qian Chang-zhao,

Tang Jia-Shi

Publication year - 2006

Publication title -

acta physica sinica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.199

H-Index - 47

ISSN - 1000-3290

DOI - 10.7498/aps.55.617

Subject(s) - bifurcation , transcritical bifurcation , saddle node bifurcation , bifurcation diagram , homoclinic bifurcation , biological applications of bifurcation theory , bifurcation theory , control theory (sociology) , period doubling bifurcation , perturbation (astronomy) , infinite period bifurcation , bogdanov–takens bifurcation , mathematics , mathematical analysis , physics , computer science , control (management) , nonlinear system , quantum mechanics , artificial intelligence

A forced system with two time-delays, including van der Pol-Duffing types, is studied. The aim is to study the primary parametrical resonance bifurcation of this system. Perturbation method is used to obtain the bifurcation equation with time-delays. Based on the bifurcation equation, co-dimension one, co-dimension two and Hope bifurcation are discussed, and the effect of time-delays on the steady state response is analyzed by numerical methods. It is indicated that the primary resonance bifurcation can be well controlled by time-delays feedback.

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