TY - JOUR
T1 - Strange attractors for asymptotically zero maps
AU - Joshi, Yogesh
AU - Blackmore, Denis
N1 - Funding Information:
Y. Joshi would like to thank his department for support of his work on this paper, and D. Blackmore is indebted to NSF Grant CMMI 1029809 for partial support of his efforts in this collaboration. The authors wish also to thank the reviewers for their insightful and detailed constructive criticism, which led to a marked improvement in the original manuscript.
Publisher Copyright:
© 2014 Elsevier Ltd. All rights reserved.
PY - 2014/1
Y1 - 2014/1
N2 - 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.
AB - 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.
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U2 - 10.1016/j.chaos.2014.08.005
DO - 10.1016/j.chaos.2014.08.005
M3 - Article
AN - SCOPUS:84907195432
SN - 0960-0779
VL - 68
SP - 123
EP - 138
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
ER -