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Amplitude control of a limit cycle in a coupled van der Pol system. (English) Zbl 1175.34038

Summary: In order to control the amplitude of a limit cycle of a coupled van der Pol system, feedback controllers are designed. The control equations of the weakly nonlinear systems are obtained by using an approximate method, and the relationship between the amplitude of the limit cycle and the control parameter is derived. Hence, the amplitude of the limit cycle can be controlled effectively. The method may also be applied to other coupled van der Pol systems.

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34H05 Control problems involving ordinary differential equations
93B52 Feedback control
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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