Abstract
One 3D fractional-order chaotic system with only one locally asymptotically stable equilibrium is reported. To verify the chaoticity, the maximum Lyapunov exponent (MAXLE) with respect to the fractional-order and chaotic attractors are obtained by numerical calculation for this system. Furthermore, by linear scalar controller consisting of a single state variable, one control scheme for stabilization of the 3D fractional-order chaotic system is suggested. The numerical simulations show the feasibility of the control scheme.
Highlights
Fractional-order calculus is an old branch of mathematics, which can be dated back to the 17th century [1, 2]
One control scheme for stabilization of this fractional-order chaotic system is suggested via linear scalar controller consisting of a single state variable
In order to stabilize this fractional-order chaotic system, one control scheme is proposed via linear scalar controller consisting of a single state variable
Summary
Fractional-order calculus is an old branch of mathematics, which can be dated back to the 17th century [1, 2]. A simple three-dimensional autonomous chaotic system [17] with only one stable node-focus equilibrium has been reported by Wang and Chen. Some integer order chaotic systems with stable node-focus equilibrium have been presented. One control scheme for stabilization of this fractional-order chaotic system is suggested via linear scalar controller consisting of a single state variable. The organization of this paper is as follows: in Section 2, a new fractional-order chaotic system with only one stable equilibrium is presented, and the maximum Lyapunov exponent and chaotic attractors are obtained.
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