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arXiv · 1302.5904

Dynamics of large cooperative pulsed-coupled networks

Eleonora Catsigeras
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Abstract

We study the deterministic dynamics of networks N composed by m non identical, mutually pulse-coupled cells. We assume weighted, asymmetric and positive (cooperative) interactions among the cells, and arbitrarily large values of m. We consider two cases of the network's graph: the complete graph, and the existence of a large core (i.e. a large complete subgraph). First, we prove that the system periodically eventually synchronizes with a natural "spiking period" \ p >=1, and that if the cells are mutually structurally identical or similar, then the synchronization is complete (p= 1) . Second, we prove that the amount of information H that N generates or processes equals log p. Therefore, if N completely synchronizes, the information is null. Finally, we prove that N protects the cells from their risk of death.

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Eleonora Catsigeras. 2013-02-24. Dynamics of large cooperative pulsed-coupled networks. https://doi.org/10.3934/jdg.2014.1.255

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