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Symmetric functional differential equations and neural networks with memory
Authors:Jianhong Wu
Institution:Department of Mathematics and Statistics, York University, North York, Ontario, Canada M3J 1P3
Abstract:We establish an analytic local Hopf bifurcation theorem and a topological global Hopf bifurcation theorem to detect the existence and to describe the spatial-temporal pattern, the asymptotic form and the global continuation of bifurcations of periodic wave solutions for functional differential equations in the presence of symmetry. We apply these general results to obtain the coexistence of multiple large-amplitude wave solutions for the delayed Hopfield-Cohen-Grossberg model of neural networks with a symmetric circulant connection matrix.

Keywords:Periodic solution  delay differential equation  wave  symmetry  neural network  equivariant degree  global bifurcation  
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