A Generalized 2-D Model for Fully Bounded Chaotic Attractors and Chaotic Seas

A Generalized 2-D Model for Fully Bounded Chaotic Attractors and Chaotic Seas

Zeraoulia Elhadj (Department of Mathematics, University of Tébessa, Tébessa, Algeria)
Copyright: © 2012 |Pages: 4
DOI: 10.4018/jalr.2012040105

Abstract

The aim of this paper is to present a fully bounded 2-D model for chaotic attractors or chaotic seas. The relevance of this result is that there are some specific examples of bounded chaotic attractors or chaotic seas. There is no rigorous proof of this property for a general form of mappings.
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A Fully Bounded 2-D Model For Chaotic Attractors Or Chaotic Seas

In this paper, we propose the following 2-D map as a model for a fully bounded map:

jalr.2012040105.m01
(1) where jalr.2012040105.m02 is the bifurcation parameter. The map (1) is characterized by three nonlinearities jalr.2012040105.m03 and jalr.2012040105.m04 These functions must satisfy the conditions:

jalr.2012040105.m05with jalr.2012040105.m06 for all jalr.2012040105.m07 and some values of jalr.2012040105.m08. Assume also that the values of the functions jalr.2012040105.m09) and jalr.2012040105.m10 are finite for all jalr.2012040105.m11. The map (1) is dissipative when jalr.2012040105.m12for alljalr.2012040105.m13otherwise the map is conservative.

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