Article ID Journal Published Year Pages File Type
767320 Communications in Nonlinear Science and Numerical Simulation 2011 12 Pages PDF
Abstract

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 equilibria. 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 equilibrium 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 unidirectional linear error feedback coupling approach. Numerical results show the effectiveness of the theoretical analysis.

Related Topics
Physical Sciences and Engineering Engineering Mechanical Engineering
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