Evidence of universality for the May-Wigner stability theorem for random networks with local dynamics.
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.
Sinha
Sitabhra
S
The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai-600 113, India. sitabhra@imsc.res.in
Sinha
Sudeshna
S
D000222:Adaptation, Physiological; D000818:Animals; D005075:Biological Evolution; D003163:Competitive Behavior / Q000502:physiology*; D003198:Computer Simulation; D017753:Ecosystem; D019143:Evolution, Molecular; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D011157:Population Dynamics; D011158:Population Growth; D016019:Survival Analysis; D015996:Survival Rate