The DOI matches its Crossref record; 22 of the 22 references it cites were found in a registry or an index.
Symmetric functional differential equations and neural networks with memory
Open accessAbstract
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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Cites
Partial Differential Equations
(1988) · Lecture Notes in Mathematics · doi:10.1007/bfb0082920 · Cited by 23,383
Neural networks and physical systems with emergent collective computational abilities.
Hopfield, J. J. (1982) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.79.8.2554 · Cited by 19,270
Rudin, W. (1973) · Cited by 13,740
Hopfield, J. J. (1984) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.81.10.3088 · Cited by 6,918
Theory of Functional Differential Equations
Hale, J. K. (1977) · Applied Mathematical Sciences · doi:10.1007/978-1-4612-9892-2 · Cited by 6,870
Craggs, J. W. (1973) · The Mathematical Gazette · doi:10.2307/3615195 · Cited by 4,164
Singularities and Groups in Bifurcation Theory
Golubitsky, M., Stewart, I., & Schaeffer, D. G. (1988) · Applied Mathematical Sciences · doi:10.1007/978-1-4612-4574-2 · Cited by 2,958
Cohen, M. A., & Grossberg, S. (1983) · IEEE Transactions on Systems, Man, and Cybernetics · doi:10.1109/tsmc.1983.6313075 · Cited by 2,541
Theory and applications of Hopf bifurcation
Hassard, B., Kazarinoff, N. D., & Wan, Y. (1981) · Cambridge University Press eBooks · Cited by 2,520
Some global results for nonlinear eigenvalue problems
Rabinowitz, P. H. (1971) · Journal of Functional Analysis · doi:10.1016/0022-1236(71)90030-9 · Cited by 1,846
Metadata
- Authors
- Wu, J.
- Venue
- Transactions of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Published
- 1998
- Volume
- 350
- Issue
- 12
- Pages
- 4799-4838
- ISSN
- 0002-9947 (ISSN-L)
- 1088-6850
- OpenAlex
- W1552317631
- Cited by
- 441
- References
- 22
- FWCI
- 9.07
- Type
- journal article
- Language
- en
- Open access
- bronze
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
