具有多共存吸引子的忆阻混沌系统分析与同步

Analysis and synchronization of memristive chaotic system with multiple coexisting attractors

以经典混沌理论为基础,构造了一个新的具有多共存吸引子的忆阻混沌系统。对其进行基本动力学特性分析,设计模拟电路进行仿真验证,同时还探究了该忆阻混沌系统的同步控制问题。研究结果表明该系统的运动轨迹同时受到系统参数和初始状态的影响,由此可产生单涡卷和双涡卷两种混沌吸引子,倍周期分岔,周期共存、混沌吸引子共存以及分岔共存等现象。电路仿真实验结果与理论分析和数值仿真的结果基本吻合,为忆阻混沌系统的实际应用奠定一定基础。根据现有理论提出合适的自适应控制器实现了同步,同时辨识出系统的未知参数,通过数值仿真验证了该控制方法的有效性。

Based on the classic chaos theory,a new memristive chaotic system with multiple coexistent attractors was constructed.The basic dynamic characteristics of the system was analyzed,an analog circuit was designed for simulation,and the synchronization control of the system was explored.The results show that the trajectory of the system is affected by the system parameters and the initial state,which can produce two kinds of chaotic attractors including single scroll and double scroll,period doubling bifurcation,period coexistence,chaotic attractor coexistence,bifurcation coexistence and other phenomena.The circuit simulation results are basically consistent with the theoretical analysis and numerical simulation results,which lays a certain foundation for the practical application of the memristive chaotic system.According to the existing theory,a suitable adaptive controller was proposed to achieve synchronization.At the same time,the unknown parameters of the system were identified.The effectiveness of the control method was verified by the numerical simulation.