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Periodic travelling waves in a family of deterministic cellular automata
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UNSPECIFIED (1996) Periodic travelling waves in a family of deterministic cellular automata. PHYSICA D, 95 (3-4). pp. 319-335. ISSN 0167-2789.
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Abstract
Reaction-diffusion equations whose kinetics contain a stable limit cycle are an established class of models for a range of biological and chemical systems. In this paper I construct a family of deterministic cellular automata, with nine states, which are qualitatively similar to oscillatory reaction-diffusion equations, in that their rules reflect both local oscillations and spatial diffusion. The automata can be crudely interpreted as models of predator-prey interactions, and I show that the behaviour following local perturbation of the prey-only state in one space dimension is very similar in the automata and in standard reaction-diffusion models for predator-prey systems. In particular, in many cases, invasion of prey by predators leaves behind periodic travelling waves in the wake of invasion. I study in detail these periodic plane waves in the automaton, by explicitly investigating periodic solutions of the difference equation governing travelling waves. I show that the automaton has many different periodic wave solutions, and I compare their properties with those of periodic wave solutions of reaction-diffusion systems. The basic conclusion is that included amongst the periodic waves in the automaton are a family of solutions which mimic quite closely the properties of reaction-diffusion periodic waves.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Journal or Publication Title: | PHYSICA D | ||||
Publisher: | ELSEVIER SCIENCE BV | ||||
ISSN: | 0167-2789 | ||||
Official Date: | 1 September 1996 | ||||
Dates: |
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Volume: | 95 | ||||
Number: | 3-4 | ||||
Number of Pages: | 17 | ||||
Page Range: | pp. 319-335 | ||||
Publication Status: | Published |
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