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Chaos in the fractional order periodically forced complex Duffing’s oscillators. (English) Zbl 1088.37046

Summary: The occurrence of fractional-order chaotic dynamics have been intensively studied over the last ten years in a large number of real dynamical systems of physical nature. However, a similar study has not yet been carried out for fractional-order chaotic dynamical systems in the complex domain. In this paper, we numerically study the chaotic behaviors in the fractional-order symmetric and nonsymmetric periodically forced complex Duffing’s oscillators. We find that chaotic behaviors exist in the fractional-order periodically forced complex Duffing oscillators with orders less than 4. Our results are validated by the existence of positive maximal Lyapunov exponent.

MSC:

37N05 Dynamical systems in classical and celestial mechanics
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
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