Chaos in the fractional order periodically forced complex Duffing's oscillators

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 non-symmetric periodically forced complex Duffing's oscillators. We find that chaotic behaviors exist in the fractional-order periodically forced complex Duffing's oscillators with orders less than 4. Our results are validated by the existence of positive maximal Lyapunov exponent.