dorsal/arxiv
View SchemaMany Attractors, Long Chaotic Transients, and Failure in Small-World Networks of Excitable Neurons
| Authors | Hermann Riecke, Alex Roxin, Santiago Madruga, Sara A. Solla |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0701047 |
| URL | https://arxiv.org/abs/q-bio/0701047 |
| DOI | 10.1063/1.2743611 |
Abstract
We study the dynamical states that emerge in a small-world network of recurrently coupled excitable neurons through both numerical and analytical methods. These dynamics depend in large part on the fraction of long-range connections or `short-cuts' and the delay in the neuronal interactions. Persistent activity arises for a small fraction of `short-cuts', while a transition to failure occurs at a critical value of the `short-cut' density. The persistent activity consists of multi-stable periodic attractors, the number of which is at least on the order of the number of neurons in the network. For long enough delays, network activity at high `short-cut' densities is shown to exhibit exceedingly long chaotic transients whose failure-times averaged over many network configurations follow a stretched exponential. We show how this functional form arises in the ensemble-averaged activity if each network realization has a characteristic failure-time which is exponentially distributed.
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"abstract": "We study the dynamical states that emerge in a small-world network of\nrecurrently coupled excitable neurons through both numerical and analytical\nmethods. These dynamics depend in large part on the fraction of long-range\nconnections or `short-cuts\u0027 and the delay in the neuronal interactions.\nPersistent activity arises for a small fraction of `short-cuts\u0027, while a\ntransition to failure occurs at a critical value of the `short-cut\u0027 density.\nThe persistent activity consists of multi-stable periodic attractors, the\nnumber of which is at least on the order of the number of neurons in the\nnetwork. For long enough delays, network activity at high `short-cut\u0027 densities\nis shown to exhibit exceedingly long chaotic transients whose failure-times\naveraged over many network configurations follow a stretched exponential. We\nshow how this functional form arises in the ensemble-averaged activity if each\nnetwork realization has a characteristic failure-time which is exponentially\ndistributed.",
"arxiv_id": "q-bio/0701047",
"authors": [
"Hermann Riecke",
"Alex Roxin",
"Santiago Madruga",
"Sara A. Solla"
],
"categories": [
"q-bio.NC",
"cond-mat.dis-nn",
"nlin.CD",
"physics.bio-ph"
],
"doi": "10.1063/1.2743611",
"title": "Many Attractors, Long Chaotic Transients, and Failure in Small-World Networks of Excitable Neurons",
"url": "https://arxiv.org/abs/q-bio/0701047"
},
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