Strange Attractors for Asymptotically Zero Maps
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 . 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.
Cite
@article{arxiv.1310.5417,
title = {Strange Attractors for Asymptotically Zero Maps},
author = {Yogesh Joshi and Denis Blackmore},
journal= {arXiv preprint arXiv:1310.5417},
year = {2015}
}
Comments
21 pages, 6 figures, reported on in a special session on difference equations at the AMS meeting at Temple University, Oct. 11, 12