From limit cycles to periodic orbits through ultradiscretisation

R. Willox, A. Ramani, J. Satsuma and B. Grammaticos

Physica A: Statistical Mechanics and its Applications, 2007, vol. 385, issue 2, 473-486

Abstract: We examine the transition between discrete and ultradiscrete (cellular-automaton-like) systems, the dynamics of which exhibit limit cycles. Motivated by results obtained previously for three-dimensional systems, we consider here a more manageable two-dimensional model. We show that one can follow the changes in dynamics of the system when a parameter that tunes the discrete–ultradiscrete transition is varied. In particular we explain the phenomenon of the splitting of a discrete limit cycle to a profusion of periodic orbits at the ultradiscrete limit.

Keywords: Limit cycles; Cellular automata; Periodic orbits; Discrete systems (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:385:y:2007:i:2:p:473-486

DOI: 10.1016/j.physa.2007.07.002

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