Amari模型單峰解和多峰解的存在性與穩定性

doi:10.6846%2fTKU.2007.00319

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Title:	Amari模型單峰解和多峰解的存在性與穩定性
Other Titles:	Existence and stability of single-bump and multi-bump solutions of an amari model
Authors:	林素心;Lin, Su-shing
Contributors:	淡江大學數學學系博士班張慧京
Keywords:	中心流形;不變葉理;漸進相;多峰解;center manifold;invariant foliation;asymptotic phase;multi-bump solution
Date:	2007
Issue Date:	2010-01-11 02:52:44 (UTC+8)
Abstract:	Amari模型乃是模擬包含激勵及抑制作用的單層齊次神經網路之積分微分方程式，本篇論文主要是討論此模型單峰解和多峰解的存在性及穩定性。若將幾個shift夠大的單峰解組合在一起，便可製造出多峰解。若將此積分微分方程式視為在無限維中之動態系統，則利用耦函數可計算出Frechet導數在單峰解和多峰解的分譜，以便討論其動態性質。應用中心流形理論及葉理可以探討多峰解的漸進相之穩定性。數值模擬的結果亦會發現一些分岐現象的產生。最後，當耦函數滿足某些特定條件時，我們找到2-峰解存在的充分條件。 We consider the existence and stability of single-bump and multi-bump solutions of an Amari model, a class of integral-differential equations modeling a single layer of homogeneous neural network with both excitatory and inhibitory neuron. Existence results are obtained by combining several shifts of a one-bump solution. Dynamical properties are obtained by considering the equation as an infinite dimensional dynamical systems and the spectrum of single-bump and multi-bump solutions in terms of the coupling functions. The center manifold theory and its foliation are used to show exponential stability with asymptotic phase for multi-bump solutions. Numerical results for some possible bifurcation phenomena are also presented. Finally, we give a sufficient condition such that a 2-bump solution exists while the coupling function satisfying some particular conditions.
DOI:	10.6846%2fTKU.2007.00319
Appears in Collections:	[Graduate Institute & Department of Mathematics] Thesis

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