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Absolute stability of global pattern formation and parallel memory storage by competitive neural networks
Abstract
Systems that are competitive and possess symmetric interactions admit a global Lyapunov function. However, a global Lyapunov function whose equilibrium set can be effectively analyzed has not yet been discovered. It remains an open question whether the Lyapunov function approach, which requires a study of equilibrium points, or an alternative global approach, such as the Lyapunov functional approach, which sidesteps a direct study of equilibrium points will ultimately handle all of the physically important cases.
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Cites
The Hypercycle: A principle of natural self-organization Part B: The abstract hypercycle
Eigen, M., & Schuster, P. (1978) · Naturwissenschaften · doi:10.1007/bf00420631 · Cited by 702
Cited by
Zhang, K. (1996) · The Journal of Neuroscience · doi:10.1523/jneurosci.16-06-02112.1996 · Cited by 1,001
Accurate Path Integration in Continuous Attractor Network Models of Grid Cells
Burak, Y., & Fiete, I. R. (2009) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000291 · Cited by 779
Supervised neural networks for the classification of structures
Sperduti, A., & Starita, A. (1997) · IEEE Transactions on Neural Networks · doi:10.1109/72.572108 · Cited by 666
Beggs, J. M., & Plenz, D. (2004) · The Journal of Neuroscience · doi:10.1523/jneurosci.0540-04.2004 · Cited by 587
Symmetric functional differential equations and neural networks with memory
Wu, J. (1998) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-98-02083-2 · Cited by 441
Metadata
- Authors
- Cohen, M. A., & Grossberg, S.
- Venue
- IEEE Transactions on Systems, Man, and Cybernetics
- Published
- 1983-09
- Volume
- SMC-13
- Issue
- 5
- Pages
- 815-826
- ISSN
- 0018-9472 (ISSN-L)
- 2168-2909
- OpenAlex
- W2062210787
- Cited by
- 2,541
- References
- 1
- FWCI
- 21.17
- Type
- journal article
- Language
- en
- Open access
- closed
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- Cohen, M. A., & Grossberg, S. (1983). Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions on Systems, Man, and Cybernetics. https://doi.org/10.1109/tsmc.1983.6313075
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