本文選題：分?jǐn)?shù)階神經(jīng)系統(tǒng) + 憶阻��； 參考：《湖北師范大學(xué)》2017年碩士論文

【摘要】：作為一種特定的動(dòng)力系統(tǒng),神經(jīng)動(dòng)力學(xué)系統(tǒng)是近年來(lái)研究的一個(gè)熱門話題.我們看到的大部分系統(tǒng)是整數(shù)階系統(tǒng),現(xiàn)實(shí)生活中的例子,要求系統(tǒng)是任意階的,所以研究分?jǐn)?shù)階系統(tǒng)很有應(yīng)用價(jià)值.本文對(duì)基于憶阻分?jǐn)?shù)階神經(jīng)網(wǎng)絡(luò)的反同步進(jìn)行了研究,設(shè)計(jì)了幾類線性反饋控制器,利用不連續(xù)動(dòng)力系統(tǒng)理論、拉普拉斯變換、Mittag-Leffler函數(shù)方法及Leibniz法則,獲得了分?jǐn)?shù)階α屬于0α1情形下該系統(tǒng)反同步的充分條件.并且通過(guò)數(shù)據(jù)仿真進(jìn)行了分析和論證.首先,本文介紹了基于憶阻分?jǐn)?shù)階神經(jīng)系統(tǒng)的研究背景、目的及意義,闡述了神經(jīng)網(wǎng)絡(luò)模型及本文所做的主要工作.其次,設(shè)計(jì)了兩類線性反饋控制器,運(yùn)用帶有不連續(xù)右端的分?jǐn)?shù)階微分方程的相關(guān)理論、拉普拉斯變換、Mittag-Leffler函數(shù),研究了基于憶阻分?jǐn)?shù)階神經(jīng)網(wǎng)絡(luò)的全局Mittag-Leffler反同步,并利用數(shù)據(jù)仿真驗(yàn)證了結(jié)果的有效性.再次,運(yùn)用帶有不連續(xù)右端的分?jǐn)?shù)階微分方程的相關(guān)理論、Leibniz法則,在合適的線性反饋控制器下,獲得了基于憶阻分?jǐn)?shù)階神經(jīng)網(wǎng)絡(luò)的全局O(t-α)反同步的充分條件,并利用數(shù)據(jù)仿真驗(yàn)證了結(jié)果的有效性.最后,對(duì)本文做了總結(jié),并提出了一些可以進(jìn)一步研究的問(wèn)題.
[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 偽 belonging to 0 偽 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- 偽 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.
【學(xué)位授予單位】：湖北師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

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本文編號(hào)：1928753