Period-doubling route to chaos for a global variable of a probabilistic automata network
- 21 August 1992
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 25 (16) , L1009-L1014
- https://doi.org/10.1088/0305-4470/25/16/004
Abstract
As a function of a parameter characterizing the degree of mixing of site values, the density of nonzero sites of some one-dimensional cellular automata is shown to exhibit a sequence of period-doubling bifurcations and to behave chaotically when the degree of mixing is sufficiently large. The automata network rules which are considered appear to be useful to model complex systems, as in epidemiology, in which the motion of the individuals is believed to play an important role.Keywords
This publication has 11 references indexed in Scilit:
- Automata network SIR models for the spread of infectious diseases in populations of moving individualsJournal of Physics A: General Physics, 1992
- Collective Behaviors in Spatially Extended Systems with Local Interactions and Synchronous UpdatingProgress of Theoretical Physics, 1992
- Noisy collective behaviour in deterministic cellular automataPhysica A: Statistical Mechanics and its Applications, 1992
- Particlelike structures and their interactions in spatiotemporal patterns generated by one-dimensional deterministic cellular-automaton rulesPhysical Review A, 1991
- Block transformations of one-dimensional deterministic cellular automaton rulesJournal of Physics A: General Physics, 1991
- Evidence of Collective Behaviour in Cellular AutomataEurophysics Letters, 1991
- Order of the transition versus space dimension in a family of cellular automataPhysical Review A, 1989
- Scaling for External Noise at the Onset of ChaosPhysical Review Letters, 1981
- Scaling Theory for Noisy Period-Doubling Transitions to ChaosPhysical Review Letters, 1981
- Quantitative universality for a class of nonlinear transformationsJournal of Statistical Physics, 1978