Open AccessGeneralized synchronization of two different unidirectional coupled Lorenz systems
Author(s) -
Xiaojuan Li,
Zhi-Hong Xu,
Xie Qing-Chun,
Bing Wang
Publication year - 2010
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.59.1532
Subject(s) - stability theory , type (biology) , lorenz system , zero (linguistics) , synchronization (alternating current) , boundary (topology) , limit (mathematics) , stability (learning theory) , mathematics , physics , mathematical analysis , topology (electrical circuits) , nonlinear system , computer science , combinatorics , attractor , quantum mechanics , ecology , linguistics , philosophy , machine learning , biology
The generalized synchronization GS of two different unidirectional coupled Lorenz systems is studied. According to the method of auxiliary-system, by using the theories of stability and the boundary of the responsed system, a sufficient criterion is rigorously proven. Furthermore, based on the modified system approach, GS is classified into three types, the first type,the second type and the third type of GS when the modified system has an asymptotically stable equilibrium of zero solution, asymptotically stable equilibrium of non-zero solution, asymptotically stable limit cycles, respectively. Moreover, using the Routh-Hurwitz theorem to analyze the stability of equilibrium of the modified system, the existence of the first type and the second type of GS are strictly theoretically proved. Numerical simulations show the effectiveness of the method.