| Title |
Integrate and fire neural networks, piecewise contractive maps and limit cycles
|
|---|---|
| Published in |
Journal of Mathematical Biology, July 2012
|
| DOI | 10.1007/s00285-012-0560-7 |
| Pubmed ID | |
| Authors |
Eleonora Catsigeras, Pierre Guiraud |
| Abstract |
We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the stable asymptotic dynamics consists of limit cycles. We also find sufficient conditions for the synchronization of networks containing excitatory neurons. The proofs are based on the analysis of the equivalent dynamics of a piecewise continuous Poincaré map associated to the system. We show that for efficient interactions the Poincaré map is piecewise contractive. Using this contraction property, we prove that there exist a countable number of limit cycles attracting all the orbits dropping into the stable subset of the phase space. This result applies not only to the Poincaré map under study, but also to a wide class of general n-dimensional piecewise contractive maps. |
X Demographics
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Geographical breakdown
| Country | Count | As % |
|---|---|---|
| Unknown | 1 | 100% |
Demographic breakdown
| Type | Count | As % |
|---|---|---|
| Members of the public | 1 | 100% |
Mendeley readers
The data shown below were compiled from readership statistics for 9 Mendeley readers of this research output. Click here to see the associated Mendeley record.
Geographical breakdown
| Country | Count | As % |
|---|---|---|
| Israel | 1 | 11% |
| Unknown | 8 | 89% |
Demographic breakdown
| Readers by professional status | Count | As % |
|---|---|---|
| Professor > Associate Professor | 2 | 22% |
| Student > Ph. D. Student | 2 | 22% |
| Other | 1 | 11% |
| Professor | 1 | 11% |
| Researcher | 1 | 11% |
| Other | 1 | 11% |
| Unknown | 1 | 11% |
| Readers by discipline | Count | As % |
|---|---|---|
| Physics and Astronomy | 4 | 44% |
| Agricultural and Biological Sciences | 1 | 11% |
| Medicine and Dentistry | 1 | 11% |
| Neuroscience | 1 | 11% |
| Engineering | 1 | 11% |
| Other | 0 | 0% |
| Unknown | 1 | 11% |
Attention Score in Context
This research output has an Altmetric Attention Score of 1. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 06 August 2013.
All research outputs
#18,342,133
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Outputs from Journal of Mathematical Biology
#442
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Outputs of similar age
#124,769
of 163,040 outputs
Outputs of similar age from Journal of Mathematical Biology
#4
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