Attractors for discrete periodic dynamical systems.
type: Item
instance of: scholarly article
title: Attractors for discrete periodic dynamical systems.
zbMATH Open document ID: 1035.37020
DOI: 10.1016/S0022-247X(03)00417-7
author: John E. Franke
author: James F. Selgrade
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-11-16T00:00:00Z
review text: The paper introduces a notion of an attractor for a discrete time periodic dynamical system, given by~\(p\) maps \(f_0,\ldots,f_{p-1}\) on a metric space~\(X\), by extending the system to \(\{0,\ldots,p-1\}\times X\). It is shown that such an attractor is the union of attractors for the~\(p\) autonomous maps \(F_i=f_{p-1+i}\circ\cdots\circ f_i\), \(0\leq i\leq p\). Conditions are given under which the constituents of an attractor of a periodic perturbation of an autonomous map are homeomorphic to the attractor of this map. Several examples, some of them originating from population dynamics, are discussed. The results fit nicely into the theory of attractors for nonautonomous and for random systems, which has been developed during the last decade.
reviewed by: Hans Crauel
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 37N25
zbMATH DE Number: 2003888
zbMATH Keywords: periodic dynamical system
zbMATH Keywords: nonautonomous attractor
zbMATH Keywords: trapping region
zbMATH Keywords: periodic prey-predator system
zbMATH Keywords: periodic perturbations of autonomous systems
MaRDI profile type: Publication
cites work: Resonant population cycles in temorally fluctuating habitats
cites work: Periodic Time-Dependent Predator-Prey Systems
cites work: Two species competition in a periodic environment
cites work: Multiple attractors and resonance in periodically forced population models
cites work: Multiple attractors, saddles, and population dynamics in periodic habitats
cites work: The effect of periodic habitat fluctuations on a nonlinear insect population model
cites work: Q3137759
cites work: Q4003408
cites work: Dynamical analysis of density-dependent selection in a discrete one-island migration model
cites work: Q4888828
cites work: On the structure of attractors for discrete, periodically forced systems with applications to population models
cites work: Uniform weak implies uniform strong persistence for non-autonomous semiflows
cites work: Uniform persistence and permanence for non-autonomous semiflows in population biology
full work available at URL: s0022-247x(03)00417-7
OpenAlex ID: W2037625229
Recommended article: ATTRACTORS FOR LATTICE DYNAMICAL SYSTEMS
Recommended article: Q4455266
Recommended article: Q3753893
Recommended article: Attractors Under Discretisation
Recommended article: Stability and attractivity in discrete dynamical systems
Recommended article: Attractors and partial stability of nonlinear dynamical systems.
Recommended article: Uniform attractors of periodic and asymptotically periodic dynamical systems
Recommended article: Discrete dynamical systems and bifurcation for periodic differential equations
Recommended article: Q5150415
Recommended article: Forward Attractors in Discrete Time Nonautonomous Dynamical Systems
description: scientific article; zbMATH DE number 2003888