【摘要】：細(xì)胞神經(jīng)網(wǎng)絡(luò)是一種信息處理系統(tǒng),其特點(diǎn)是細(xì)胞之間局部連接,輸出函數(shù)是分段線性的。因此,它能夠?qū)崿F(xiàn)大規(guī)模非線性模擬電路信號(hào)的實(shí)時(shí)與并行處理,并提高運(yùn)行速度。細(xì)胞神經(jīng)網(wǎng)絡(luò)已成功應(yīng)用于優(yōu)化問題、模式識(shí)別和圖像處理等領(lǐng)域。穩(wěn)定性是細(xì)胞神經(jīng)網(wǎng)絡(luò)應(yīng)用于實(shí)際問題的前提。由于放大器有限的開關(guān)速度和電子元件中發(fā)生的錯(cuò)誤,導(dǎo)致電子神經(jīng)網(wǎng)絡(luò)中產(chǎn)生時(shí)滯。而時(shí)滯常常會(huì)破壞細(xì)胞神經(jīng)網(wǎng)絡(luò)系統(tǒng)的穩(wěn)定性,甚至導(dǎo)致系統(tǒng)產(chǎn)生劇烈振蕩。對(duì)于時(shí)滯細(xì)胞神經(jīng)網(wǎng)絡(luò)的研究具有重要的理論價(jià)值和現(xiàn)實(shí)意義。借助非線性測(cè)度的方法,本文主要對(duì)幾類帶有時(shí)滯的細(xì)胞神經(jīng)網(wǎng)絡(luò)的全局指數(shù)穩(wěn)定性進(jìn)行研究,具體研究?jī)?nèi)容如下:1、研究具有多比例時(shí)滯細(xì)胞神經(jīng)網(wǎng)絡(luò)的全局指數(shù)穩(wěn)定性。通過對(duì)一類帶有無界時(shí)滯的微分不等式的穩(wěn)定性進(jìn)行研究,然后利用所得的結(jié)果,借助非線性測(cè)度方法得到該網(wǎng)絡(luò)全局指數(shù)穩(wěn)定的充分條件。2、研究具有時(shí)變時(shí)滯周期細(xì)胞神經(jīng)網(wǎng)絡(luò)的全局指數(shù)穩(wěn)定性。通過非線性測(cè)度方法以及對(duì)Halanay不等式進(jìn)行推廣,得到其穩(wěn)定的充分條件。3、對(duì)具有分布時(shí)滯周期細(xì)胞神經(jīng)網(wǎng)絡(luò)的全局指數(shù)穩(wěn)定性進(jìn)行研究,先得出一類具有分布時(shí)滯微分不等式的穩(wěn)定性條件,結(jié)合此條件和非線性測(cè)度方法,得到網(wǎng)絡(luò)全局指數(shù)穩(wěn)定的條件。4、對(duì)具有時(shí)變時(shí)滯概周期細(xì)胞神經(jīng)網(wǎng)絡(luò)的全局指數(shù)穩(wěn)定性條件進(jìn)行研究,通過非線性測(cè)度方法以及利用對(duì)Halanay不等式進(jìn)行概周期推廣的結(jié)果,得到其穩(wěn)定的一個(gè)積分平均準(zhǔn)則。最后,不同類型的細(xì)胞神經(jīng)網(wǎng)絡(luò)的例子和相應(yīng)的數(shù)值模擬被提供,以證明我們方法的有效性和結(jié)論的正確性。
[Abstract]:Cellular neural network is a kind of information processing system, which is characterized by the local connection between cells, and the output function is piecewise linear. Therefore, it can realize real-time and parallel processing of large scale nonlinear analog circuit signals, and improve the speed of operation. Cellular neural networks have been successfully applied to optimization problems, pattern recognition and image processing. Stability is the premise of the application of cellular neural networks to practical problems. Due to the limited switching speed of the amplifier and the errors in the electronic components, the delay in the electronic neural network is caused. Delay often destroys the stability of cellular neural networks and even results in severe oscillations. It has important theoretical value and practical significance for the study of delayed cellular neural networks. By means of nonlinear measure, the global exponential stability of several cellular neural networks with time delay is studied in this paper. The main contents are as follows: 1. The global exponential stability of cellular neural networks with multi-scale delay is studied. By studying the stability of a class of differential inequalities with unbounded delay, the sufficient conditions for the global exponential stability of the network are obtained by using the obtained results and the nonlinear measure method. The global exponential stability of periodic cellular neural networks with time-varying delays is studied. By means of nonlinear measure method and the extension of Halanay inequality, the sufficient conditions for its stability are obtained. 3. The global exponential stability of periodic cellular neural networks with distributed delay is studied. The stability conditions of a class of differential inequalities with distributed delay are obtained. Combined with this condition and the nonlinear measure method, the condition of global exponential stability of the network is obtained. The global exponential stability conditions of almost periodic cellular neural networks with time-varying delays are studied. By means of nonlinear measure method and the results of almost periodic generalization of Halanay inequality, an integral average criterion is obtained for its stability. Finally, examples of different types of cellular neural networks and corresponding numerical simulations are provided to verify the validity of our method and the correctness of our conclusions.
【學(xué)位授予單位】：長安大學(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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