TY - JOUR A2 - Petras, Ivo AU - Zheng, Guangchao AU - Liu, Ling AU - Liu, Chongxin PY - 2019 DA - 2019/07/22 TI - Hidden Coexisting Attractors in a Fractional-Order System without Equilibrium: Analysis, Circuit Implementation, and Finite-Time Synchronization SP - 6908607 VL - 2019 AB - In this paper, a novel three-dimensional fractional-order chaotic system without equilibrium, which can present symmetric hidden coexisting chaotic attractors, is proposed. Dynamical characteristics of the fractional-order system are analyzed fully through numerical simulations, mainly including finite-time local Lyapunov exponents, bifurcation diagram, and the basins of attraction. In particular, the system can generate diverse coexisting attractors varying with different orders, which presents ample and complex dynamic characteristics. And there is great potential for secure communication. Then electronic circuit of the fractional-order system is designed to help verify its effectiveness. What is more, taking the disturbances into account, a finite-time synchronization of the fractional-order chaotic system without equilibrium is achieved and the improved controller is proven strictly by applying finite-time stable theorem. Eventually, simulation results verify the validity and rapidness of the proposed method. Therefore, the fractional-order chaotic system with hidden attractors can present better performance for practical applications, such as secure communication and image encryption, which deserve further investigation. SN - 1024-123X UR - https://doi.org/10.1155/2019/6908607 DO - 10.1155/2019/6908607 JF - Mathematical Problems in Engineering PB - Hindawi KW - ER -