Dynamics of large cooperative pulsed-coupled networks

TL;DR

This paper analyzes the deterministic dynamics of large cooperative pulse-coupled networks, showing they synchronize periodically, generate limited information, and protect cells from death, with implications for understanding complex network behavior.

Contribution

It provides rigorous proofs of synchronization, information limits, and protective properties in large cooperative pulse-coupled networks, extending understanding of their dynamics.

Findings

Networks synchronize periodically with period p.

Complete synchronization occurs under structural similarity.

The information processed by the network is log p.

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.