基于忆阻器的分数阶非线性动力学系统设计

发布时间：2018-05-13 10:11

本文选题：分数阶 + 传递函数　；参考：《江西理工大学》2017年硕士论文

【摘要】：非线性系统吸引子个数代表着该系统的联想记忆能力,由于分数阶非线性动力学系统可以实现对吸引子个数的拓展,因此其记忆能力相对整数阶系统更好。忆阻器由于具有天然的记忆功能,利用忆阻器同样能够增大非线性系统的存储容量。本文主要是针对非线性动力学系统进行构建、仿真及稳定性分析,深入地研究传统三维整数及分数阶广义洛伦兹系统,设计了一种新的组合型分数阶基本单元电路,将其应用于异元异构分数阶整体电路仿真中。同时设计了忆阻函数多项式分别为可变整数指数幂及可变分数指数幂的一般忆阻器模型,研究了其在简约混沌电路系统中的应用。本文重点研究内容如下:1.构建传统三维整数阶广义Lorenz系统,通过对其进行动力学特性分析,理论上证实系统混沌吸引子的存在性;为整数阶系统构造电路原理图,电路仿真结果显示该系统具有物理可实现性。将整数阶系统替换为相应地分数阶系统,同时引入基于波特图的线性近似法计算出一系列(0,1)之间以0.025递减的传递函数表达式,并参考4种已有的分数阶单元电路,设计了一种新的组合型分数阶单元电路,并将其与其他四种单元电路组合应用于分数阶整体电路原理图中,实现了异元异构分数阶电路的仿真,证实其电路设计的可靠性及多样性。引入两个分数阶稳定性定理,利用该定理对所设计的系统开展稳定性分析。2.设计忆阻函数多项式为连续可变整数指数幂的一般忆阻器模型,将其应用于最简混沌电路系统并进行数值仿真,此时系统能够产生一个混沌吸引子,表明其具有混沌特性;研究线性参数对系统混沌特性的影响,设计该一般忆阻器模型的电路原理图,通过数值及电路仿真验证忆阻器的三个本质特征。将一般忆阻器模型的忆阻函数多项式指数幂由连续可变正整数拓展至分数,同样研究系统能否产生吸引子以及系统状态是否受其线性参数的影响;同时基于指数、对数运算电路设计乘方运算电路,将其应用于分数指数幂一般忆阻器的电路设计中,分数指数幂的忆阻函数可能在实际应用中更具价值。将基于一般忆阻器的简约混沌电路系统转变为分数阶系统,同时对其进行不同阶次组合的数值仿真。理论分析和数值、电路仿真均说明了分数阶系统及分数指数幂一般忆阻器的物理可实现性及电路设计的有效性,实验成果对传统非线性动力学系统拥有一定参考价值及意义。
[Abstract]:The number of attractors represents the associative memory ability of the nonlinear system. Because the fractional nonlinear dynamical system can extend the number of attractors, its memory ability is better than that of the integer order system. Because of its natural memory function, the memory capacity of nonlinear systems can also be increased by using it. In this paper, a new combinatorial fractional order basic unit circuit is designed to construct, simulate and analyze the nonlinear dynamics system, deeply study the traditional three-dimensional integer and fractional generalized Lorentz system. It is applied to the whole circuit simulation of heterogeneous fractional order. At the same time, a general memory model with variable integer exponential power and variable fractional exponential power is designed, and its application in reduced chaotic circuit system is studied. The main contents of this paper are as follows: 1: 1. The existence of chaotic attractor of traditional three-dimensional integer order generalized Lorenz system is theoretically proved by analyzing its dynamic characteristics, and the circuit schematic diagram is constructed for integer order system. The circuit simulation results show that the system has physical realizability. The integer order system is replaced by the corresponding fractional order system, and a series of expressions of transfer function with 0.025 decrement between them are calculated by introducing a linear approximation method based on Porter's graph, and four kinds of fractional order cell circuits are referred to. A new combinatorial fractional order circuit is designed and applied to the whole circuit schematic diagram of fractional order, and the simulation of heterogeneous fractional order circuit is realized. The reliability and diversity of the circuit design are verified. Two fractional order stability theorems are introduced to analyze the stability of the designed system. A general memory model with a polynomial of memory function as a continuous variable integer exponent power is designed. The model is applied to the simplest chaotic circuit system and numerically simulated. In this case, the system can produce a chaotic attractor, which shows that it has chaotic characteristics. The influence of linear parameters on the chaotic characteristics of the system is studied. The circuit schematic diagram of the general model is designed, and the three essential characteristics of the demultiplexer are verified by numerical and circuit simulation. In this paper, the polynomial exponential power of memory function is extended from a continuous variable positive integer to a fraction to study whether the system can produce attractors and whether the state of the system is affected by its linear parameters. The logarithmic operation circuit is designed and applied to the circuit design of the general demertiplexer of the fractional exponential power. The memory function of the fractional exponential power may be more valuable in practical application. The reduced chaotic circuit system based on the general amnesia is transformed into a fractional order system, and the numerical simulation of different order combinations is carried out at the same time. Theoretical analysis, numerical simulation and circuit simulation show the physical realizability of fractional order system and fractional exponential power general resistor, and the effectiveness of circuit design. The experimental results have certain reference value and significance for traditional nonlinear dynamic systems.
【学位授予单位】：江西理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN60

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