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.
Original language | English (US) |
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Pages (from-to) | 123-138 |
Number of pages | 16 |
Journal | Chaos, Solitons and Fractals |
Volume | 68 |
DOIs | |
State | Published - Jan 2014 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- General Mathematics
- General Physics and Astronomy
- Applied Mathematics