基于多涡卷混沌系统的电路设计及应用

发布时间：2019-05-28 12:07

【摘要】：在非线性系统中混沌是一类特殊的物理现象,具有初始状态敏感性、类噪声性、自相似性等特点。它广泛地存在于物理学、生命科学,以及社会科学等领域,并与相对论、量子力学共同被誉为20世纪人类最伟大的三大成就。目前伴随非线性理论的不断发展,混沌逐渐成为信息安全方面一个重要的研究领域。与一般的混沌结构不同,多涡卷混沌系统的运动轨迹拥有更为丰富的相空间结构、更加复杂的非线性行为及多变的密钥空间,并且其运动轨迹还可以在同一个吸引子中的不同混沌涡卷之间进行随机跳变,这些特性使得多涡卷混沌系统在实际工程中具有十分广阔的应用前景。而如何设计出新型多涡卷混沌模型,并将其进行物理应用,已引起国内外专家学者的广泛关注。本论文重点探讨了多涡卷混沌模型对应的结构特性。首先,在Chua’s电路的模型上,采用简单的Heaviside方程得到了一种拉伸式多涡卷混沌模型,并分析了其混沌状态下的动力学特性。其次,还搭建了该系统的PSPICE电路。通过线性耦合法,构建了拉伸式多涡卷混沌系统对应的同步模型,并将其引入保密通信中,从而验证了新系统在实际应用中的有效性及可行性。紧接着,探究了混沌系统与多翼吸引子之间的内在联系,并将非奇非偶函数引入3维多翼蝴蝶混沌系统,从而改变了传统多翼蝴蝶型混沌模型相对单一的设计理念。同时,分析了系统的动力学特性包括:相空间的拓扑结构,系统变量生成的时域波形,功率谱,Lyapunov指数以及复杂度等。其电路实验与理论模拟基本相同,进而为多翼蝴蝶型混沌模型的构建给出了新的思路。最后,考虑到当前多涡卷混沌模型的电路结构较为复杂,一个电路模型一般只能生成一种吸引子结构。本论文结合电路工作原理设计出一种3维自治混沌开关系统,实现了单个涡卷混沌模型的双混沌吸引子控制结构,从而提高了单个混沌模型在实际工程中的利用率。通过理论推导、数值仿真探究了其对应的非线性动力学特性及其在开关控制下混沌吸引子结构的变化情况。同时,设计了新系统的同步方案,并实现了信号的加密、解密,从而为多涡卷混沌系统的物理设计及应用提供了一定的理论基础。
[Abstract]:Chaos is a special kind of physical phenomenon in nonlinear systems, which has the characteristics of initial state sensitivity, noise-like property, self-similarity and so on. It widely exists in physics, life science, social science and other fields, and, together with relativity and quantum mechanics, is known as the three greatest achievements of mankind in the 20th century. With the continuous development of nonlinear theory, chaos has gradually become an important research field in information security. Different from the general chaotic structure, the trajectory of multi-scroll chaotic system has more abundant phase spatial structure, more complex nonlinear behavior and changeable key space. Moreover, the trajectory of the system can also jump randomly between different chaotic scrolls in the same index. these characteristics make the multi-scroll chaotic system have a very broad application prospect in practical engineering. However, how to design a new multi-scroll chaotic model and apply it to physics has attracted extensive attention of experts and scholars at home and abroad. In this paper, the structural characteristics of the multi-scroll chaotic model are discussed. Firstly, on the model of Chua's circuit, a stretched multi-scroll chaotic model is obtained by using simple Heaviside equation, and the dynamic characteristics of the model in chaotic state are analyzed. Secondly, the PSPICE circuit of the system is also built. Through the linear coupling method, the synchronization model of the stretched multi-scroll chaotic system is constructed and introduced into the secure communication, which verifies the effectiveness and feasibility of the new system in practical application. Then, the internal relationship between chaotic system and multi-wing attractor is explored, and the non-odd and non-even function is introduced into the three-dimensional multi-wing butterfly chaotic system, thus changing the design concept of the traditional multi-wing butterfly chaos model. At the same time, the dynamic characteristics of the system are analyzed, including the topological structure of phase space, the time domain waveform generated by system variables, power spectrum, Lyapunov index and complexity. The circuit experiment and theoretical simulation are basically the same, and then a new idea for the construction of multi-wing butterfly chaotic model is given. Finally, considering that the circuit structure of the current multi-scroll chaotic model is more complex, a circuit model can only generate one attractive substructure. In this paper, a three-dimensional autonomous chaotic switch system is designed according to the working principle of the circuit, and the double chaotic Attractor control structure of a single scroll chaos model is realized, which improves the utilization rate of a single chaotic model in practical engineering. Through theoretical derivation, the corresponding nonlinear dynamic characteristics and the variation of chaotic attractive substructure under switch control are investigated by numerical simulation. At the same time, the synchronization scheme of the new system is designed, and the signal encryption and decryption are realized, which provides a certain theoretical basis for the physical design and application of multi-scroll chaotic system.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O415.5

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