Dynamic transitions in Domany-Kinzel cellular automata on small-world network
1 Centre for Modeling and Simulation, University of Pune, Pune 411007, India
2 PG Department of Physics, University of Amran, Yemen
3 PG Department of Physics, Rashtrasant Tukdoji Maharaj Nagpur University, Nagpur 440033, India
Revised: 3 May 2013
Published online: 11 July 2013
We study Domany-Kinzel cellular automata on small-world network. Every link on a one dimensional chain is rewired and coupled with any node with probability p. We observe that, the introduction of long-range interactions does not remove the critical character of the model and the system still exhibits a well-defined phase transition to absorbing state. In case of directed percolation (DP), we observe a very anomalous behavior as a function of size. The system shows long lived metastable states and a jump in order parameter. This jump vanishes in thermodynamic limit and we recover second-order transition. The critical exponents are not equal to the mean-field values even for large p. However, for compact directed percolation(CDP), the critical exponents reach their mean-field values even for small p.
© EDP Sciences, Springer-Verlag, 2013