A Simple Approach to Achieve Modified Projective Synchronization between Two Different Chaotic Systems

A Simple Approach to Achieve Modified Projective Synchronization between Two Different Chaotic Systems

A new approach, the projective system approach, is proposed to realize modified projective synchronization between two different chaotic systems. By simple analysis of trajectories in the phase space, a projective system of the original chaotic systems is obtained to replace the errors system to jud...

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Main Authors: Lei Wang, Bin Zhen, Jian Xu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:The Scientific World Journal
Online Access:http://dx.doi.org/10.1155/2013/568194
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spelling doaj-123aaf2b9e8e4c67b92462ce37e1a7ee2020-11-25T01:11:21ZengHindawi LimitedThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/568194568194A Simple Approach to Achieve Modified Projective Synchronization between Two Different Chaotic SystemsLei Wang0Bin Zhen1Jian Xu2College of Hydraulic and Environmental Engineering, China Three Gorges University, Yichang 443002, ChinaCollege of Hydraulic and Environmental Engineering, China Three Gorges University, Yichang 443002, ChinaSchool of Aerospace and Mechanics Engineering, Tongji University, Shanghai 200092, ChinaA new approach, the projective system approach, is proposed to realize modified projective synchronization between two different chaotic systems. By simple analysis of trajectories in the phase space, a projective system of the original chaotic systems is obtained to replace the errors system to judge the occurrence of modified projective synchronization. Theoretical analysis and numerical simulations show that, although the projective system may not be unique, modified projective synchronization can be achieved provided that the origin of any of projective systems is asymptotically stable. Furthermore, an example is presented to illustrate that even a necessary and sufficient condition for modified projective synchronization can be derived by using the projective system approach.http://dx.doi.org/10.1155/2013/568194
collection DOAJ
language English
format Article
sources DOAJ
author Lei Wang
Bin Zhen
Jian Xu
spellingShingle Lei Wang
Bin Zhen
Jian Xu
A Simple Approach to Achieve Modified Projective Synchronization between Two Different Chaotic Systems
The Scientific World Journal
author_facet Lei Wang
Bin Zhen
Jian Xu
author_sort Lei Wang
title A Simple Approach to Achieve Modified Projective Synchronization between Two Different Chaotic Systems
title_short A Simple Approach to Achieve Modified Projective Synchronization between Two Different Chaotic Systems
title_full A Simple Approach to Achieve Modified Projective Synchronization between Two Different Chaotic Systems
title_fullStr A Simple Approach to Achieve Modified Projective Synchronization between Two Different Chaotic Systems
title_full_unstemmed A Simple Approach to Achieve Modified Projective Synchronization between Two Different Chaotic Systems
title_sort simple approach to achieve modified projective synchronization between two different chaotic systems
publisher Hindawi Limited
series The Scientific World Journal
issn 1537-744X
publishDate 2013-01-01
description A new approach, the projective system approach, is proposed to realize modified projective synchronization between two different chaotic systems. By simple analysis of trajectories in the phase space, a projective system of the original chaotic systems is obtained to replace the errors system to judge the occurrence of modified projective synchronization. Theoretical analysis and numerical simulations show that, although the projective system may not be unique, modified projective synchronization can be achieved provided that the origin of any of projective systems is asymptotically stable. Furthermore, an example is presented to illustrate that even a necessary and sufficient condition for modified projective synchronization can be derived by using the projective system approach.
url http://dx.doi.org/10.1155/2013/568194
work_keys_str_mv AT leiwang asimpleapproachtoachievemodifiedprojectivesynchronizationbetweentwodifferentchaoticsystems
AT binzhen asimpleapproachtoachievemodifiedprojectivesynchronizationbetweentwodifferentchaoticsystems
AT jianxu asimpleapproachtoachievemodifiedprojectivesynchronizationbetweentwodifferentchaoticsystems
AT leiwang simpleapproachtoachievemodifiedprojectivesynchronizationbetweentwodifferentchaoticsystems
AT binzhen simpleapproachtoachievemodifiedprojectivesynchronizationbetweentwodifferentchaoticsystems
AT jianxu simpleapproachtoachievemodifiedprojectivesynchronizationbetweentwodifferentchaoticsystems
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