2013/10/21 by Yogesh M. Joshi, Yogesh Joshi, Denis Blackmore · 8 citations
Mathematics · Physics and Astronomy · #Artificial intelligence #Attractor #Chaos control and synchronization #Chaotic #Computer science #Discrete mathematics #Dynamical systems theory #Euclidean geometry #Geometry #Infinity #Invariant (physics) #Iterated function #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear system #Physics #Pure mathematics #Quantum chaos and dynamical systems #Set (abstract data type) #Stability theory #Variety (cybernetics) #Zero (linguistics) #math.DS #msc:37D45 #msc:37E99 #msc:92D25 #msc:92D40
paper · pdf · doi:10.1016/j.chaos.2014.08.005
published in Chaos Solitons & Fractals 68, 123-138 (Elsevier BV) · 21 pages, 6 figures, reported on in a special session on difference equations at the AMS meeting at Temple University, Oct. 11, 12
arxiv created 2013/10/21 · openalex publication_date 2014/09/07 · arxiv updated 2015/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.