BIDIRECTIONALLY COUPLED SYNCHRONIZATION OF THE GENERALIZEDLORENZ SYSTEMS
Juan CHEN, Jun-an LU, Xiaoqun WU
作者信息+
School of Mathematics and Statistics, Wuhan University, Wuhan
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BIDIRECTIONALLY COUPLED SYNCHRONIZATION OF THE GENERALIZEDLORENZ SYSTEMS
Juan CHEN, Jun-an LU, Xiaoqun WU
Author information+
School of Mathematics and Statistics, Wuhan University, Wuhan
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文章历史+
收稿日期
修回日期
出版日期
2008-09-16
1900-01-01
2011-06-25
发布日期
2011-08-17
摘要
Wu, Chen, and Cai (2007) investigated chaos synchronization of two identical generalized Lorenz systems unidirectionally coupled by a linear state error feedback controller. However, bidirectional coupling in real life such as complex dynamical networks is more universal. This paper provides a unified method for analyzing chaos synchronization of two bidirectionally coupled generalized Lorenz systems. Some sufficient synchronization conditions for some special coupling matrices (diagonal matrices, so-called dislocated coupling matrices, and so on) are derived through rigorously mathematical theory. In particular, for the classical Lorenz system, the authors obtain synchronization criteria which only depend upon its parameters using new estimation of the ultimate bounds of Lorenz system (Chaos, Solitons, and Fractals, 2005). The criteria are then applied to four typical generalized Lorenz systems in the numerical simulations for verification.
Abstract
Wu, Chen, and Cai (2007) investigated chaos synchronization of two identical generalized Lorenz systems unidirectionally coupled by a linear state error feedback controller. However, bidirectional coupling in real life such as complex dynamical networks is more universal. This paper provides a unified method for analyzing chaos synchronization of two bidirectionally coupled generalized Lorenz systems. Some sufficient synchronization conditions for some special coupling matrices (diagonal matrices, so-called dislocated coupling matrices, and so on) are derived through rigorously mathematical theory. In particular, for the classical Lorenz system, the authors obtain synchronization criteria which only depend upon its parameters using new estimation of the ultimate bounds of Lorenz system (Chaos, Solitons, and Fractals, 2005). The criteria are then applied to four typical generalized Lorenz systems in the numerical simulations for verification.
Juan CHEN
, Jun-an LU
, Xiaoqun WU. , {{custom_author.name_cn}}.
BIDIRECTIONALLY COUPLED SYNCHRONIZATION OF THE GENERALIZEDLORENZ SYSTEMS. 系统科学与复杂性(英文), 2011, 24(3): 433-448 https://doi.org/10.1007/s11424-010-8323-2
Juan CHEN
, Jun-an LU
, Xiaoqun WU. , {{custom_author.name_en}}.
BIDIRECTIONALLY COUPLED SYNCHRONIZATION OF THE GENERALIZEDLORENZ SYSTEMS. Journal of Systems Science and Complexity, 2011, 24(3): 433-448 https://doi.org/10.1007/s11424-010-8323-2
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