English, Article edition: DOUBLE HOPF BIFURCATION FOR STUARTâLANDAU SYSTEM WITH NONLINEAR DELAY FEEDBACK AND DELAY-DEPENDENT PARAMETERS SUQI MA; QISHAO LU; S. JOHN HOGAN

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Bookmark: http://trove.nla.gov.au/version/134216
Physical Description
  • article
Language
  • English

Edition details

Title
  • DOUBLE HOPF BIFURCATION FOR STUARTâLANDAU SYSTEM WITH NONLINEAR DELAY FEEDBACK AND DELAY-DEPENDENT PARAMETERS
Author
  • SUQI MA
  • QISHAO LU
  • S. JOHN HOGAN
Physical Description
  • article
Notes
  • A StuartâLandau system under delay feedback control with the nonlinear delay-dependent parameter e-pÏ is investigated. A geometrical demonstration method combined with theoretical analysis is developed so as to effectively solve the characteristic equation. Multi-stable regions are separated from unstable regions by allocations of Hopf bifurcation curves in (p,Ï) plane. Some weak resonant and non-resonant oscillation phenomena induced by double Hopf bifurcation are discovered. The normal form for double Hopf bifurcation is deduced. The local dynamical behavior near double Hopf bifurcation points are also clarified in detail by using the center manifold method. Some states of two coexisting stable periodic solutions are verified, and some torus-broken procedures are also traced.
  • StuartâLandau system, double Hopf bifurcation, time delay, feedback control
  • RePEc:wsi:acsxxx:v:10:y:2007:i:04:p:423-448
Language
  • English
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