Constructing a new chaotic system based on the Šilnikov criterion
type: Item
instance of: scholarly article
title: Constructing a new chaotic system based on the Šilnikov criterion
zbMATH Open document ID: 1053.37015
DOI: 10.1016/S0960-0779(03)00251-0
author: Tianshou Zhou
author: Guanrong Chen
author: Qi-Gui Yang
published in: Chaos, Solitons and Fractals
publication date: 2004-07-01T00:00:00Z
review text: Based on the Šilnikov criterion, the authors construct a new chaotic system of quadratic polynomial ordinary differential equations in three dimensions, which has a single equilibrium point. The authors rigorously prove that this system satisfies all conditions stated in the Šilnikov theorem, which clearly reveals its chaos formation mechanism and implies the existence of Smale horseshoes. Moreover, the authors show that their simulation demonstrated there is a route to chaos through period-doubling bifurcations.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 37D15
zbMATH DE Number: 2077294
zbMATH Keywords: Šilnikov cirterion
zbMATH Keywords: Smale horseshoes
zbMATH Keywords: chaos
zbMATH Keywords: period-doubling bifurcations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2077294