新混沌系统及其分数阶系统的自适应同步控制
New chaotic system and the adaptive synchronization control of its fractional order system

研究一个存在共存吸引子的混沌系统及相应的分数阶系统的自适应同步问题. 首先, 提出了一个新的具有双翼和四翼吸引子共存的混沌系统, 对系统的动力学特性进行了分析, 找到了系统的拓扑马蹄和拓扑熵, 从而验证了系统具有混沌特性; 然后, 根据该系统构建了一个亦存在两个孤立的双翼吸引子以及四翼吸引子的分数阶系统.最后, 采用分数阶Lyapunov稳定性理论以及自适应控制方法, 对分数阶系统的自适应同步问题进行了研究. 仿真结果表明, 控制参数k越大, 系统同步速度越快; 控制参数λ越大, 系统参数识别的速度越快.
A novel chaotic system with coexisting attractors and the adaptive synchronization control of the corresponding fractional order chaotic system are studied. Firstly, a novel chaotic system with coexisting attractors of double-wing and four-wing is proposed. The dynamic characteristics of the system are analyzed, and the topological horseshoe and topological entropy of the system are found, which verifies that the system is chaotic. Secondly, a fractional order system with two isolated double-wing and four-wing attractors is constructed based on this system. Finally, the adaptive synchronization problem of the fractional order system is investigated by means of fractional order Lyapunov stability theory and adaptive control method. Simulation results show that the larger the control parameter k, the faster the system synchronization speed, and the larger the control parameter λ, the faster the identification of the system parameters.