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arXiv · 1310.5417

Strange Attractors for Asymptotically Zero Maps

Yogesh Joshi·Denis Blackmore
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Abstract

A discrete dynamical system in Euclidean m-space generated by the iterates of an asymptotically zero map f, satisfying f(x) goes to zero as x goes to infinity, 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.

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Yogesh Joshi, Denis Blackmore. 2013-10-21. Strange Attractors for Asymptotically Zero Maps. https://doi.org/10.1016/j.chaos.2014.08.005

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