Dynamics with choice

Lev Kapitanski, Sanja Živanović

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Dynamics with choice is a generalization of discrete-time dynamics where instead of the same evolution operator at every time step there is a choice of operators to transform the current state of the system. Many real-life processes studied in chemical physics, engineering, biology and medicine, from autocatalytic reaction systems to switched systems to cellular biochemical processes to malaria transmission in urban environments, exhibit the properties described by dynamics with choice. We study the long-term behaviour in dynamics with choice. We prove very general results on the existence and properties of global compact attractors in dynamics with choice. In addition, we study the dynamics with restricted choice when the allowed sequences of operators correspond to subshifts of the full shift. One of the practical consequences of our results is that when the parameters of a discrete-time system are not known exactly and/or are subject to change due to internal instability or a strategy or Nature's intervention, the long-term behaviour of the system may not be correctly described by a system with 'averaged' values for the parameters. There may be a Gestalt effect.

Original languageEnglish (US)
Pages (from-to)163-186
Number of pages24
JournalNonlinearity
Volume22
Issue number1
DOIs
StatePublished - Jan 1 2009

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operators
Malaria
Subshift
Evolution Operator
Switched Systems
Discrete-time Systems
Operator
biology
medicine
Medicine
Biology
Attractor
Discrete-time
Physics
engineering
Transform
Engineering
Internal
physics
shift

ASJC Scopus subject areas

  • Applied Mathematics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Dynamics with choice. / Kapitanski, Lev; Živanović, Sanja.

In: Nonlinearity, Vol. 22, No. 1, 01.01.2009, p. 163-186.

Research output: Contribution to journalArticle

Kapitanski, L & Živanović, S 2009, 'Dynamics with choice', Nonlinearity, vol. 22, no. 1, pp. 163-186. https://doi.org/10.1088/0951-7715/22/1/009
Kapitanski, Lev ; Živanović, Sanja. / Dynamics with choice. In: Nonlinearity. 2009 ; Vol. 22, No. 1. pp. 163-186.
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