Chaos, feedback control and synchronization of a fractional-order] modified Autonomous Van der Pol-Duffing circuit

摘要

In this work, stability analysis of the fractional-order modified Autonomous Van der Pol-Duffing (MAVPD) circuit is studied using the fractional Routh-Hurwitz criteria. A necessary condition for this system to remain chaotic is obtained. It is found that chaos exists in this system with order less than 3. Furthermore, the fractional Routh-Hurwitz conditions are used to control chaos in the proposed fractional-order system to its equilib-ria. Based on the fractional Routh-Hurwitz conditions and using specific choice of linear controllers, it is shown that the fractional-order MAVPD system is controlled to its equilib-rium points; however, its integer-order counterpart is not controlled. Moreover, chaos synchronization of MAVPD system is found only in the fractional-order case when using a specific choice of nonlinear control functions. This shows the effect of fractional order on chaos control and synchronization. Synchronization is also achieved using the unidirec-tional linear error feedback coupling approach. Numerical results show the effectiveness of the theoretical analysis.