Some predictability in one-dimensional chaotic dynamical systems arising in population models
type: Item
instance of: scholarly article
title: Some predictability in one-dimensional chaotic dynamical systems arising in population models
zbMATH Open document ID: 0595.58040
DOI: 10.1016/0196-8858(85)90011-9
author: Jun Kigami
published in: Advances in Applied Mathematics
publication date: 1985-01-01T00:00:00Z
review text: Consider the iteration (discrete, one dimensional dynamical system) \(x_{n+1}=f(x_ n)\) where f is a nonnegative unimodal map. The sojourning time n(f,x) is the maximal number of iterations which don't carry the system with initial state x above the value of the unique maximal point of the system. The sojourning time corresponding to this maximal point k (f(k)\(\geq f(x))\) is denoted by N(f). According to the author the degree of chaos is measured by N(f). This is justified by the fact that the topological entropy of f is, loosely speaking, increasing with N(f). Fluctuating systems and predictability of sojourning times of fluctuating systems are studied. In some systems depending on a parameter the degree of chaos may increase while the sojourning time may become more predictable. The results may be applied, e.g., to the system \(x_{n+1}=x_ n\exp (r(1-x_ n/c)).\)
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 3958303
zbMATH Keywords: iteration
zbMATH Keywords: discrete, one dimensional dynamical system
zbMATH Keywords: sojourning time
zbMATH Keywords: predictability
zbMATH Keywords: fluctuating systems
zbMATH Keywords: degree of chaos
reviewed by: M. Farkas
MaRDI profile type: Publication
full work available at URL: 0196-8858(85)90011-9
OpenAlex ID: W2045342554
cites work: Topological Entropy
cites work: Erratum to "Entropy for Group Endomorphisms and Homogeneous Spaces"
cites work: The dynamics of density dependent population models
cites work: Period Three Implies Chaos
cites work: Simple mathematical models with very complicated dynamics
cites work: On the resolution of chaos in population models
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description: scientific article; zbMATH DE number 3958303