English

Dynamics of large cooperative pulsed-coupled networks

Dynamical Systems 2016-06-28 v2 Neurons and Cognition

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.

Keywords

Cite

@article{arxiv.1302.5904,
  title  = {Dynamics of large cooperative pulsed-coupled networks},
  author = {Eleonora Catsigeras},
  journal= {arXiv preprint arXiv:1302.5904},
  year   = {2016}
}

Comments

We introduced the changes suggested by the referees. To appear in Journal of Dynamics and Games http://aimsciences.org/journals/home.jsp?journalID=26, Vol. 1 N. 2, aprox. April 2014. Premat 2013/160 (Prepublicaciones de la Universidad de la Rep\'ublica) http://premat.fing.edu.uy/papers/2013/160.pdf