Bifurcations of mutually coupled equations in random graphs

Número: 
10
Ano: 
2014
Autor: 
Eduardo Garibaldi
Tiago Pereira
Abstract: 

We study the behavior of solutions of mutually coupled equations in heterogeneous random graphs. Heterogeneity means that some equations receive many inputs whereas most of the equations are given only with a few connections. Starting from a situation where the isolated equations are unstable, we prove that the a heterogeneous interaction structure leads to the appearance of stable subspaces of solutions. Moreover, we show that, for certain classes of heterogeneous networks, increasing the strength of interaction leads to a cascade of bifurcations in which the dimension of the stable subspace of solu-tions increases. We explicitly determine the bifurcation scenario in terms of the graph structure.

Keywords: 
bifurcation
coupled equations
dichotomies
random graphs
Mathematics Subject Classification 2010 (MSC 2010): 
05C80; 34C15; 34F05; 34F10; 37C10; 60B20
Observação: 
09/14
Arquivo: