基于忆阻分数阶神经网络的反同步

发布时间：2018-05-24 10:40

本文选题：分数阶神经系统 + 忆阻　；参考：《湖北师范大学》2017年硕士论文

【摘要】：作为一种特定的动力系统,神经动力学系统是近年来研究的一个热门话题.我们看到的大部分系统是整数阶系统,现实生活中的例子,要求系统是任意阶的,所以研究分数阶系统很有应用价值.本文对基于忆阻分数阶神经网络的反同步进行了研究,设计了几类线性反馈控制器,利用不连续动力系统理论、拉普拉斯变换、Mittag-Leffler函数方法及Leibniz法则,获得了分数阶α属于0α1情形下该系统反同步的充分条件.并且通过数据仿真进行了分析和论证.首先,本文介绍了基于忆阻分数阶神经系统的研究背景、目的及意义,阐述了神经网络模型及本文所做的主要工作.其次,设计了两类线性反馈控制器,运用带有不连续右端的分数阶微分方程的相关理论、拉普拉斯变换、Mittag-Leffler函数,研究了基于忆阻分数阶神经网络的全局Mittag-Leffler反同步,并利用数据仿真验证了结果的有效性.再次,运用带有不连续右端的分数阶微分方程的相关理论、Leibniz法则,在合适的线性反馈控制器下,获得了基于忆阻分数阶神经网络的全局O(t-α)反同步的充分条件,并利用数据仿真验证了结果的有效性.最后,对本文做了总结,并提出了一些可以进一步研究的问题.
[Abstract]:As a specific dynamic system, neurodynamic system is a hot topic in recent years. Most of the systems we see are integer order systems. Examples in real life require the system to be arbitrary, so it is very valuable to study fractional order systems. In this paper, the inverse synchronization based on the memory fractional neural network is studied, and several kinds of linear feedback controllers are designed. Using the theory of discontinuous dynamic system, the Laplace transform Mittag-Leffler function method and the Leibniz's rule are used. A sufficient condition for de-synchronization of the system with fractional order 伪 belonging to 0 伪 1 is obtained. And through the data simulation to carry on the analysis and the demonstration. Firstly, this paper introduces the research background, purpose and significance of the fractional neural system based on amnesia, and describes the neural network model and the main work done in this paper. Secondly, two kinds of linear feedback controllers are designed. Using the theory of fractional differential equation with discontinuous right end, the Laplace transform Mittag-Leffler function is used to study the global Mittag-Leffler inverse synchronization based on the memory fractional neural network. The validity of the results is verified by data simulation. Thirdly, using the Leibniz rule of fractional differential equations with discontinuous right end, a sufficient condition of global Ot- 伪 inverse synchronization based on memory fractional neural network is obtained under the suitable linear feedback controller. The validity of the results is verified by data simulation. Finally, this paper is summarized and some problems that can be further studied are put forward.
【学位授予单位】：湖北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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