A Fractional-Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller. (25th June 2018)

• Record Type: Journal Article
• Authors: Zhou, Ping; Ke, Meihua; Zhu, Peng
• Other Names: Pham Viet-Thanh Academic Editor.
• Is Part Of: Complexity. Volume 2018(2018)
• Publication Date: 2018-06-25
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2018/4192824
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : 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.