A Fractional-Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller

الملخص EN

A 3D fractional-order nonlinear system with coexisting chaotic attractors is proposed in this paper.

The necessary condition of the existence chaos is q≥0.8477.

The fractional-order system exhibits chaotic attractors with the order as low as 2.5431.

The largest Lyapunov exponent varying as fractional order q is given.

Furthermore, there are the coexisting “positive attractor” and “negative attractor” in this fractional-order chaotic system, and the necessary condition for “positive attractor” and “negative attractor” is obtained.

Meanwhile, a control scheme for the stabilization of the unstable equilibrium is suggested via a single state variable linear controller.

Numerical results show that the control scheme is valid.