Evidence of universality for the May-Wigner stability theorem for random networks with local dynamics

Details Evidence of universality for the May-Wigner stability theorem for random networks with local dynamics Evidence of universality for the May-Wigner stability theorem for random networks with local dynamics

2004-02-02

arxiv.org/abs/nlin/0402002v2

Physical Review E (Rapid Communications), 71 (2005) 020902

Nonlinear Sciences

Adaptation and Self-Organizing Systems

4 pages, 4 figures, minor textual revisions in response to referee comments

Scientific paper

10.1103/PhysRevE.71.020902

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.

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