Study On The Chaos, Its Control And Synchronization In Fractional Order Dynamic Systems

The dynamics of fractional order systems have attracted increasing attentions in recent years. In this thesis, we numerically study the chaotic behaviors of the fractional order nonlinear dynamical systems, and address the problems of chaotic control and synchronization for autonomous nonlinear systems.The main originality in this paper can be summarized as below: 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 thesis, we numerically study the chaotic phenomena occuring in the fractional-order symmetric and non-symmetric periodically forced complex Duffing's oscillators. We found that chaotic behaviors exist in the fractional-order periodically forced complex DufTing's oscillators with orders less than 4. The lowest order we found for chaos to exist in such systems is 2.8. Our results are justified by the existence of positive maximal Lyapunov exponent. Also we study the chaotic behaviors in an electronic chaotic oscillator. We found that chaos exists in the fractional order electronic oscillator with order less than 3. In addition, we numerically simulate the continuance of the chaotic behavior in the electronic oscillator with orders ranging from 2.8 to 3.2. Besides, we have investigated the chaotic behaviors in a modified van der Pol oscillator . We found that chaos exists in the fractional-order modified van der Pol oscillator with order less than 3 and the lowest order we found for chaos to exist in such system is 2.4.