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Asymptotic Behavior Of Differentiable Dynamical Systems And Applications In Neural Networks

Posted on:2003-04-24Degree:DoctorType:Dissertation
Country:ChinaCandidate:L S WangFull Text:PDF
GTID:1100360065960779Subject:Operational Research and Cybernetics
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This dissertation consists of three chapters.In chapter 1, we have studied attractor, invariant set, attracting set and stability of partial functional differential equations by using Sobolev space and Banach space theory and recommending a set of operative symbol and operator method. The research method is practical and original. Moreover, we have obtained an estimate of the Hausdorff dimension of the attractor for damped nonautonomous wave equations.In chapter 2, asymptotic behavior for four classes of Hopfield neural networks with delays have been discussed by employing nonlinear functional analysis, topological degree theory, homotopy invari-ance theorem, functional inequality and Liapunov functional method. The methods determining the asymptotic and exponential stability of the neural networks in this paper are better the popular methods. Some results in this chapter include the results which have been presented by many researchers. Other results are new and original.Chapter 3 is devoted to equistability and equiboundedness of matrix differential equations by making use of the symbol property of the matrix Liapunov function and its Dini derivate on specific set. The methods discussing the asymptotic behavior of matrix differential equations are less man - made artifcial and more practical than the methord combining Liapunov function with generalized comparison theorem in [178].
Keywords/Search Tags:Differentiable dynamical systems, Hopfield neural networks, attrator, Hausdorff dimension, invariant set, global attracting set, stability, nonlinear functional, semigroups of operator, Sobolev space, Banach space, topological degree, Liapunov functional
PDF Full Text Request
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