Symmetric functional differential equations and neural networks with memory
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- by Jianhong Wu PDF
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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.References
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Additional Information
- Jianhong Wu
- Affiliation: Department of Mathematics and Statistics, York University, North York, Ontario, Canada M3J 1P3
- MR Author ID: 226643
- Email: wujh@mathstat.yorku.ca
- Received by editor(s): September 13, 1995
- Additional Notes: Research partially supported by the Natural Sciences and Engineering Research Council of Canada.
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 350 (1998), 4799-4838
- MSC (1991): Primary 34K15, 34K20, 34C25
- DOI: https://doi.org/10.1090/S0002-9947-98-02083-2
- MathSciNet review: 1451617