Dynamic transitions in Domany-Kinzel cellular automata on small-world network |
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Authors: | A. V. Mahajan M. Ali Saif P. M. Gade |
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Affiliation: | 11956. Centre for Modeling and Simulation, University of Pune, Pune, 411007, India 21956. PG Department of Physics, University of Amran, Amran, Yemen 31956. PG Department of Physics, Rashtrasant Tukdoji Maharaj Nagpur University, Nagpur, 440033, India
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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. |
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