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Chaos control in Duffing system. (English) Zbl 1091.37013
Summary: Analytical and numerical results concerning the inhibition of chaos in Duffing’s equation with two weak forcing excitations are presented. We theoretically give parameter-space regions by using Melnikov’s function, where chaotic states can be suppressed. The intervals of initial phase difference between the two excitations for which chaotic dynamics can be eliminated are given. Meanwhile, the influence of the phase difference on Lyapunov exponents for different frequencies is investigated. Numerical simulation results show the consistence with the theoretical analysis and the chaotic motions can be controlled to period-motions by adjusting parameter of suppressing excitation.

MSC:
37D45Strange attractors, chaotic dynamics
93D15Stabilization of systems by feedback
34C28Complex behavior, chaotic systems (ODE)
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References:
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