Dynamic transitions in small world networks: approach to equilibrium limit.
We study the transition to phase synchronization in a model for the spread of infection defined in a small world network. It was shown [Phys. Rev. Lett. 86, 2909 (2001)] that the transition occurs at a finite degree of disorder p, unlike equilibrium models where systems behave as random networks even at infinitesimal p in the infinite-size limit. We examine this system under variation of a parameter determining the driving rate and show that the transition point decreases as we drive the system more slowly. Thus it appears that the transition moves to p=0 in the very slow driving limit, just as in the equilibrium case.
Gade
Prashant M
PM
Centre for Modelling and Simulation, University of Pune, Ganeshkhind, Pune, 411 007, India. gade@unipune.ernet.in
Sinha
Sudeshna
S
D000818:Animals; D003141:Communicable Diseases / Q000453:epidemiology* / Q000503:physiopathology*; D003198:Computer Simulation; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D004198:Disease Susceptibility / Q000453:epidemiology* / Q000503:physiopathology*; D017753:Ecosystem; D006801:Humans; D008954:Models, Biological; D011157:Population Dynamics