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- Title
DESIGNING HOPF BIFURCATIONS INTO NONLINEAR DISCRETE-TIME SYSTEMS VIA FEEDBACK CONTROL.
- Authors
Guilin Wen; Daolin Xu
- Abstract
Hopf bifurcations lead to limit circles that exhibit oscillatory behaviors in nonlinear dynamical systems. Building a specified limit circle into nonlinear systems by control enables us to achieve preferred dynamical performance in the systems. This paper reports a general control method for generating a variety of specified Hopf bifurcations at a desired parameter location. The proposed control law is applicable to nonresonance, weak resonance, strong resonance, or degenerate cases. It allows us to flexibly operate and manipulate the control of Hopf bifurcations. The discrete washout filters are used for the feedback controller. The feedback control gains are derived from the critical conditions and stability conditions of Hopf bifurcations by means of the center manifold method and normal form technique. Numerical experiments indicate that the control method is effective.
- Subjects
NONLINEAR systems; SYSTEMS theory; RESONANCE; BIFURCATION theory; NUMERICAL solutions to nonlinear differential equations; STABILITY (Mechanics); OSCILLATIONS
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2004, Vol 14, Issue 7, p2283
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127404010679