一个新的分数阶混沌系统的翼倍增及滑模同步

首先，提出了一个新的分数阶混沌系统，通过对系统第二个等式的线性项x作绝对值运算，并分析了其唯一的参数k，该参数在一定区间内取值时可将混沌吸引子由两个翼的结构变换为四翼的拓扑结构，从而实现翼倍增. 其次，分别采用Matlab和Multisim对新的分数阶系统及其翼倍增系统进行了数值模拟和电路仿真，电路仿真结果和数值模拟结果相一致. 最后，基于滑模变结构控制理论和分数阶稳定性定理，为新的分数阶系统及其翼倍增系统设计了新的分数阶积分滑模控制器实现系统的同步，仿真结果和理论分析相一致，证实了所设计滑模控制器的有效性. 关键词： 分数阶 翼倍增 滑模控制 同步

A new double-wing fractional-order chaotic system and its synchronization by sliding mode

Firstly, a new fractional-order chaotic system is proposed. When the linear term x in the second formula of the system was replaced by its absolute value, the range of its unique parameter k that makes the wing of the original system doubled is explored in detail. Furthermore, the numerical simulation and the circuit simulation of the original system and its double-wing system are achieved via Matlab and Multisim software respectively. Finally, based on sliding mode control theory and stability theory in fractional calculus, a new sliding mode controller is designed to realize the synchronization of the new system and its double-wing system respectively. Simulation results are provided to illustrate the effectiveness of the proposed scheme.
Keywords： fractional-order double-wing sliding mode control synchronization