A Proof for the Existence of Chaos in Diffusively Coupled Map Lattices with Open Boundary Conditions

We first study how to make use of the Marotto theory to prove rigorously the existence of the Li-Yorke chaos in diffusively coupled map lattices with open boundary conditions (i.e., a high-dimensional discrete dynamical system). Then, the recent 0-1 test for chaos is applied to confirm our theoretic...

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Main Authors:	Li-Guo Yuan, Qi-Gui Yang
Format:	Article
Language:	English
Published:	Hindawi Limited 2011-01-01
Series:	Discrete Dynamics in Nature and Society
Online Access:	http://dx.doi.org/10.1155/2011/174376

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spelling	doaj-4e5b5793b9e4458783d230bf4dec74812020-11-24T20:45:30ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2011-01-01201110.1155/2011/174376174376A Proof for the Existence of Chaos in Diffusively Coupled Map Lattices with Open Boundary ConditionsLi-Guo Yuan0Qi-Gui Yang1School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, ChinaSchool of Mathematical Sciences, South China University of Technology, Guangzhou 510640, ChinaWe first study how to make use of the Marotto theory to prove rigorously the existence of the Li-Yorke chaos in diffusively coupled map lattices with open boundary conditions (i.e., a high-dimensional discrete dynamical system). Then, the recent 0-1 test for chaos is applied to confirm our theoretical claim. In addition, we control the chaotic motions to a fixed point with delay feedback method. Numerical results support the theoretical analysis.http://dx.doi.org/10.1155/2011/174376
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Li-Guo Yuan Qi-Gui Yang
spellingShingle	Li-Guo Yuan Qi-Gui Yang A Proof for the Existence of Chaos in Diffusively Coupled Map Lattices with Open Boundary Conditions Discrete Dynamics in Nature and Society
author_facet	Li-Guo Yuan Qi-Gui Yang
author_sort	Li-Guo Yuan
title	A Proof for the Existence of Chaos in Diffusively Coupled Map Lattices with Open Boundary Conditions
title_short	A Proof for the Existence of Chaos in Diffusively Coupled Map Lattices with Open Boundary Conditions
title_full	A Proof for the Existence of Chaos in Diffusively Coupled Map Lattices with Open Boundary Conditions
title_fullStr	A Proof for the Existence of Chaos in Diffusively Coupled Map Lattices with Open Boundary Conditions
title_full_unstemmed	A Proof for the Existence of Chaos in Diffusively Coupled Map Lattices with Open Boundary Conditions
title_sort	proof for the existence of chaos in diffusively coupled map lattices with open boundary conditions
publisher	Hindawi Limited
series	Discrete Dynamics in Nature and Society
issn	1026-0226 1607-887X
publishDate	2011-01-01
description	We first study how to make use of the Marotto theory to prove rigorously the existence of the Li-Yorke chaos in diffusively coupled map lattices with open boundary conditions (i.e., a high-dimensional discrete dynamical system). Then, the recent 0-1 test for chaos is applied to confirm our theoretical claim. In addition, we control the chaotic motions to a fixed point with delay feedback method. Numerical results support the theoretical analysis.
url	http://dx.doi.org/10.1155/2011/174376
work_keys_str_mv	AT liguoyuan aprooffortheexistenceofchaosindiffusivelycoupledmaplatticeswithopenboundaryconditions AT qiguiyang aprooffortheexistenceofchaosindiffusivelycoupledmaplatticeswithopenboundaryconditions AT liguoyuan prooffortheexistenceofchaosindiffusivelycoupledmaplatticeswithopenboundaryconditions AT qiguiyang prooffortheexistenceofchaosindiffusivelycoupledmaplatticeswithopenboundaryconditions
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A Proof for the Existence of Chaos in Diffusively Coupled Map Lattices with Open Boundary Conditions

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