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Dynamics in Neural Networks with Delays

Author: LiangJinLing
Tutor: CaoJinDe
School: Southeast University
Course: Applied Mathematics
Keywords: Neural networks delay activation function equilibrium point stability boundedness periodic solution Lyapunov functional M-matrix linear matrix inequality (LMI) Halanay inequality Hardy inequality impulse
CLC: O175
Type: PhD thesis
Year: 2006
Downloads: 733
Quote: 5
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Abstract


With the fast development of science and technology, the requirement is strenthened in the fields of automatic control, optimal computation and so on. And it is necessary to enhance the intelligent level of information processing. Essentially, it requires a further understanding of the dynamical behaviours of nonlinear dynamical systems. Since artificial neural networks are introduced to imitate the functions of the human brain (for example, the power of self-studying, applicable to complex communities, multi-objective control), it has attracted the attentions of many people for their important applications in many fields. Especially in the recent years, magazines and meetings related to the neural networks have been appeared continuously, and it has been the focus center of brain science, mathematics-physics, information science, control science and so on.Based on the Lyapunov functional method, the matrix theory, combining with the techniques of inequalities including Halanay inequality, Hardy inequality and linear matrix inequality (LMI), in this paper, dynamical behaviours of delayed neural networks, which are described by the functional differential equations, are analized such as boundedness, stability, robust stability, existence and uniqueness of periodic solutions. The organization of this paper is as follows:In the first chapter of this dissertation, the general development and several usual dynamical models of neural networks are reviewed. The importance of studying the dynamical behaviours of neural networks with delays is explained. Also the current status in delayed neural networks are introduced.In the second chapter, five classes of recurrent neural networks are investigated. In Section 2.1, a class of non-autonomous recurrent neural networks with variable coefficients and time-varying delays are analyzed via employing Yong inequality technique and Lyapunov method. Some simple sufficient conditions are given for ultimate boundedness and exponential stability of solutions for the recurrent neural networks. And the existence and stability of the periodic

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations
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