Evidence of universality for the May-Wigner stability theorem for random networks with local dynamics
arXiv:nlin/0402002 · doi:10.1103/PhysRevE.71.020902
Abstract
We consider a random network of nonlinear maps exhibiting a wide range of local dynamics, with the links having normally distributed interaction strengths. The stability of such a system is examined in terms of the asymptotic fraction of nodes that persist in a non-zero state. Scaling results show that the probability of survival in the steady state agrees remarkably well with the May-Wigner stability criterion derived from linear stability arguments. This suggests universality of the complexity-stability relation for random networks with respect to arbitrary global dynamics of the system.
arXiv comment4 pages, 4 figures, minor textual revisions in response to referee comments
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