Strange attractors for asymptotically zero maps

Yogesh Joshi and Denis Blackmore

Chaos, Solitons & Fractals, 2014, vol. 68, issue C, 123-138

Abstract: A discrete dynamical system in Euclidean m-space generated by the iterates of an asymptotically zero map f, satisfying f(x)→0 as x→∞, must have a compact global attracting set A. The question of what additional hypotheses are sufficient to guarantee that A has a minimal (invariant) subset A that is a chaotic strange attractor is answered in detail for a few types of asymptotically zero maps. These special cases happen to have many applications (especially as mathematical models for a variety of processes in ecological and population dynamics), some of which are presented as examples and analyzed in considerable detail.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:68:y:2014:i:c:p:123-138

DOI: 10.1016/j.chaos.2014.08.005

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