Transactions of the American Mathematical Society

Author(s): Jianhong Wu
Journal: Trans. Amer. Math. Soc. 350 (1998), 4799-4838.
MSC (1991): Primary 34K15, 34K20, 34C25
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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.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 34K15, 34K20, 34C25

Jianhong Wu
Affiliation: Department of Mathematics and Statistics, York University, North York, Ontario, Canada M3J 1P3
Email: wujh@mathstat.yorku.ca

DOI: 10.1090/S0002-9947-98-02083-2
PII: S 0002-9947(98)02083-2
Keywords: Periodic solution, delay differential equation, wave, symmetry, neural network, equivariant degree, global bifurcation.
Received by editor(s): September 13, 1995
Additional Notes: Research partially supported by the Natural Sciences and Engineering Research Council of Canada.
Copyright of article: Copyright 1998, American Mathematical Society

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