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Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I.
Abstract
A chain of $n + 1$ weakly coupled oscillators with a linear gradient in natural frequencies is shown to exhibit “frequency plateaus,” or sequences of oscillators having the same frequency, with a jump in frequency from one plateau to another. We first show that the equations for the coupled oscillators admit an invariant $(n + 1)$-torus on which the equations have a special form, one in which an n-dimensional subsystem is approximately invariant. We then show that when the linear gradient becomes too steep to allow phaselocking, there emerges a large-scale invariant circle in this n-dimensional system which corresponds to the existence of a pair of plateaus, and whose homotopy class within the n-torus corresponds to the position of the frequency jump. Also discussed are the effects of anisotropic and nonuniform coupling.
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Cites
The Geometry of Biological Time
Winfree, A. T. (1980) · doi:10.1007/978-3-662-22492-2 · Cited by 3,613
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Type I membranes, phase resetting curves, and synchrony
Ermentrout, B. (1996) · Neural Computation · doi:10.1162/neco.1996.8.5.979 · Cited by 1,001
Self-citationWhen inhibition not excitation synchronizes neural firing
Van Vreeswijk, C., Abbott, L. F., & Bard Ermentrout, G. (1994) · Journal of Computational Neuroscience · doi:10.1007/bf00961879 · Cited by 773
Singular perturbation theory of traveling waves in excitable media (a review)
Tyson, J. J., & Keener, J. P. (1988) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(88)90062-0 · Cited by 746
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Hansel, D., Mato, G., & Meunier, C. (1995) · Neural Computation · doi:10.1162/neco.1995.7.2.307 · Cited by 587
Metadata
- Authors
- Ermentrout, G. B., & Kopell, N.
- Venue
- SIAM Journal on Mathematical Analysis
- Published
- 1984-03
- Volume
- 15
- Issue
- 2
- Pages
- 215-237
- ISSN
- 0036-1410 (ISSN-L)
- 1095-7154
- OpenAlex
- W1980007064
- Cited by
- 453
- References
- 1
- FWCI
- 12.08
- Type
- journal article
- Language
- en
- Open access
- closed
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