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Zbl 0905.34034
Wu, Jianhong
Symmetric functional-differential equations and neural networks with memory. (English)
[J] Trans. Am. Math. Soc. 350, No.12, 4799-4838 (1998). ISSN 0002-9947; ISSN 1088-6850/e

Summary: The author establishes an analytic local Hopf bifurcation theorem and a topological global Hopf bifurcation theorem to detect the existence and to describe spatial-temporal pattern, asymptotic form and global continuation of bifurcations of periodic wave solutions to functional-differential equations with symmetry. The author applies 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.
MSC 2000:
*34C23 Bifurcation (periodic solutions)
34K13 Periodic solutions of functional differential equations
34K18 Bifurcation theory of functional differential equations
34C25 Periodic solutions of ODE
34K20 Stability theory of functional-differential equations
92B20 General theory of neural networks

Keywords: periodic solutions; delay differential equations; waves; symmetry; neural networks; equivariant degree; global bifurcation.; local; topological global; Hopf bifurcation; multiple large-amplitude wave solutions; delayed Hopfield-Cohen-Grossberg model

Cited in: Zbl 1221.37203 Zbl 1219.92065 Zbl 1205.34090 Zbl 1224.34230 Zbl 1220.34104 Zbl 1214.34074 Zbl 1210.34116 Zbl 1183.37155 Zbl 1183.37156 Zbl 1205.34089 Zbl 1201.34132 Zbl 1197.34121 Zbl 1185.34124 Zbl 1182.37035 Zbl 1178.34105 Zbl 1170.34051 Zbl 1147.34351 Zbl 1142.34370 Zbl 1132.34053 Zbl 1163.34053 Zbl 1151.34060 Zbl 1145.34042 Zbl 1141.34045 Zbl 1123.34055 Zbl 1105.34047 Zbl 1100.92015 Zbl 1090.92052 Zbl 1144.34373 Zbl 1067.34076 Zbl 1069.34104 Zbl 1231.34130

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