摘要
混沌理论是非线性科学的一个重要的分支,它揭示了自然界与人类社会中普遍存在的复杂性,架起了确定论和概率论两个理论体系之间的桥梁。由于在不同的学科领域,特别是在保密通信领域的广泛应用,混沌同步吸引了越来越多人的研究。本文利用理论推导和数值模拟相结合的方法研究了几类典型混沌系统的同步问题,及其在保密通信中的应用。主要工作如下:
简单介绍了混沌的发展历史,描述了常用的同步方法,简单说明了混沌保密通信的意义。
研究了一种新的超混沌Lorenz系统的限定时间同步问题,基于限定时间稳定性理论和Lyapunov稳定性理论,提出了一个简单的且高效的超混沌Lorenz系统的限定时间同步控制器。理论上证明了该方案可以保证误差系统全局限定时间稳定,数值模拟验证了所提方案的有效性。
基于状态观测器理论和极点配置技术,研究了一类时滞神经网络的投影同步问题,设计了一种投影同步方案,并从理论上证明了该方案可以实现一类延迟神经网络的投影同步,通过对延迟Hopfield网络和三阶细胞神经网络的数值模拟进一步验证了所提方案的有效性;研究了混沌系统全局混合投影同步问题,提出了一种新的全局混合投影同步方案,并给出了理论证明,扩展了全局混合投影同步的适用范围,通过对统一混沌系统和超混沌Rossler系统的数值模拟,验证了所提方案的有效性。
提出了一种新的用来传输模拟信号的二级混沌保密通信系统。该系统由四个重要部分构成:混沌同步,混沌调制,混沌掩盖和混沌接收。本文利用状态观测器理论实现了混沌同步,并将该混沌同步方法应用到该保密通信系统中。仿真实验证明该二级混沌保密通信系统的有效性。
Chaos theory is an important branch of nonlinear science, which reveals the universal complexity existing in the nature and human being world and builds a bridge between determine theory and probability theory. Chaos can be used in wildly fields, so over the last decade years, chaos synchronization technology has attracted more and more scholars to research, especially in secure communication field. This paper combines theoretical derivation and numerical simulation method to research some kinds of typical chaos synchronization problems and its application in secure communication. The main tasks are as follows.
Firstly, the paper simply introduces the chaotic development history, and then describes the general synchronization methods, finally explains the significance of chaos secure communication.
Secondly, this paper deals with the finite-time chaos synchronization of a new hyperchaotic Lorenz system. Based on the finite-time and Lyapunov stability theory, a simple and robust controller is proposed to realize finite-time chaos synchronization for the hyperchaotic Lorenz system. Theoretical analysis proved that the scheme can ensure the error system globally finite-time stable. Numerical simulations are provided to show the effectiveness of the proposed schemes.
Thirdly, based on the nonlinear state observer algorithm and pole placement technique, a synchronization scheme is designed. The projective synchronization of a class of delayed neural networks can be achieved by using the proposed method, and they are proved theoretically. Numerical simulations of delayed Hopfield network and three order cellular neural networks are provided to further demonstrate the effectiveness of the proposed scheme. Moreover, this paper proposes and creates a new full state hybrid projective synchronization and provides the theoretical proof, which enlarges the applied scope of full state hybrid projective synchronization. Take unified chaotic system and hyper-chaotic Rossler system for example, after numerical simulations, further validates the effectiveness of the proposed scheme.
Finally, this paper presents a new secondary chaotic secure communication system for analog signal transmissions. It contains four important parts: chaos synchronization, chaotic modulation, chaotic mask, and chaotic receiver. Based on the theory of state observer, a method of chaos synchronization is presented, and it is applied to the secondary secure communication system. Some simulation results are provided to verify the efficiency of the proposed secure communication system.
引文
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