一个具有隐藏特性的新五维超混沌系统的同步研究

发布时间：2018-07-10 08:08

本文选题：新超混沌系统 + 隐藏特性　；参考：《东北师范大学》2017年硕士论文

【摘要】：混沌作为一种复杂的运动形式,在非线性动力学中广泛存在,也以类随机现象的形式在确定性系统中出现。近年来随着学术界研究混沌现象的逐渐深入,混沌控制与同步已成为研究混沌的重要内容。由于其在物理、通信、信息科学、医学等领域的巨大应用潜力和发展前景,混沌控制与同步已成为科研界研究的热点之一。相比较低维系统,超混沌系统具有更复杂的动力学行为,因此,对于超混沌系统的控制与同步的研究更具有应用价值。隐藏吸引子是近年来新定义的一种吸引子,与传统的自激吸引子动力学特征不完全相同,因而引起了学术界的广泛关注。存在隐藏吸引子的混沌系统具有隐藏特性,近几年来隐藏特性得到学者们的一些关注。但由于具有隐藏特性的混沌系统发现时间较晚,关于其控制与同步的研究还比较少。本文基于Sprott B系统,设计出了一个只具有一个参数、没有平衡点、存在隐藏吸引子的新五维超混沌系统。首先通过理论分析,研究了具有隐藏特性的新五维超混沌系统的动力学特性,如:吸引子的维数、耗散性、吸引子的存在性、Lyapunov指数和分岔等,设计了具有隐藏特性的新超混沌系统的电路,进行了数值模拟和电路仿真并且用硬件电路实现了具有隐藏特性的新超混沌系统,验证了新超混沌系统的动力学特性及隐藏特性。然后对参数已知的具有隐藏特性的新超混沌系统运用线性反馈法、状态观测器法、自适应法、Backstepping同步法,设计出相应的控制器,并通过理论分析、数值模拟和电路实验对以上四种方法进行了分析和论证。实验结果表明具有隐藏特性的新超混沌系统均实现了同步,证明了控制器的有效性。最后,对参数未知的具有隐藏特性的新超混沌系统,运用非线性反馈法、自适应法和Backstepping法设计控制器,进行了理论分析、数值模拟和电路仿真,结果表明,具有隐藏特性的新超混沌系统实现了同步,控制器效果良好,能够对未知参数进行有效地识别。
[Abstract]:Chaos, as a complex form of motion, exists widely in nonlinear dynamics and appears in deterministic systems in the form of random phenomena. In recent years, chaotic control and synchronization have become an important internal capacity to study chaos with the academic circles. Chaotic control and synchronization have become one of the hotspots in the field of great application and development, and chaos control and synchronization have become one of the hotspots in the research field. Compared to low dimensional systems, hyperchaotic systems have more complex dynamic behavior. Therefore, it is more valuable for the study of the control and synchronization of hyperchaotic systems. The attractor, which is not exactly the same as the dynamic characteristics of the traditional self excited attractor, has aroused widespread concern in the academic circle. The chaotic system with hidden attractors has hidden characteristics. In recent years, the hidden characteristics of the chaotic system have received some attention from scholars. In this paper, based on Sprott B system, a new five dimensional hyperchaotic system with only one parameter, no balance point and hidden attractor is designed. First, the dynamic characteristics of the new five dimensional hyperchaotic system with hidden characteristics are studied by theoretical analysis, such as the dimension, dissipation and attraction of the attractor. The existence of the sub, the Lyapunov index and the bifurcation, etc., design the circuit of a new hyperchaotic system with hidden characteristics, carry out numerical simulation and circuit simulation, and implement a new hyperchaotic system with hidden characteristics with the hardware circuit, and verify the dynamic characteristics and hidden characteristics of the new hyperchaotic system. Then the parameters are known to the system. The new hyperchaotic system with hidden characteristics is designed by linear feedback, state observer, adaptive and Backstepping synchronization. Through theoretical analysis, numerical simulation and circuit experiment, the above four methods are analyzed and demonstrated. Experimental results show that the new hyperchaotic systems with hidden characteristics are realized. The validity of the controller is proved. Finally, the new hyperchaotic system with hidden characteristics with unknown parameters is designed by nonlinear feedback, adaptive method and Backstepping method. The theoretical analysis, numerical simulation and circuit simulation are carried out. The results show that the new hyperchaos system with hidden characteristics is synchronized and controlled. The effect is good, and the unknown parameters can be identified effectively.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O415.5;TP273

【参考文献】