Eur. Phys. J. Special Topics 222, 895-903 (2013)
https://doi.org/10.1140/epjst/e2013-01892-1

Regular Article

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

^a e-mail: mahajan@cms.unipune.ac.in
^b e-mail: masali73@gmail.com
^c e-mail: prashant.m.gade@gmail.com

Received: 22 March 2013
Revised: 3 May 2013
Published online: 11 July 2013

Abstract

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.