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Evidence of universality for the May-Wigner stability theorem for random networks with local dynamics
Sitabhra Sinha1, Sudeshna Sinha
1The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai-600 113, India. sitabhra@imsc.res.in
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 nonzero 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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