Open AccessProjective synchronization of a five-term hyperbolic-type chaotic system with fully uncertain parameters
Author(s) -
F. Richard Yu,
Chunhua Wang,
Yan Hu,
Yin Jin-wen
Publication year - 2012
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.61.060505
Subject(s) - synchronization of chaos , chaotic , term (time) , lemma (botany) , synchronization (alternating current) , hyperbolic function , control theory (sociology) , quadratic equation , nonlinear system , mathematics , computer science , mathematical analysis , topology (electrical circuits) , physics , control (management) , quantum mechanics , artificial intelligence , ecology , geometry , poaceae , combinatorics , biology
A new simple hyperbolic-type three-dimensional autonomous chaotic system is proposed. It is of interest that the chaotic system has only five terms which mainly rely on a nonlinear quadratic hyperbolic sine term and a quadratic cross-product term. Compared with other three-dimensional chaotic systems, the new system has not only less terms, but also a wider range of chaos when the parameter varies. Basic dynamical properties of the system are studied by numerical and theoretical analysis. Moreover the projective synchronization of the five-term hyperbolic-type chaotic system with fully uncertain parameters is also investigated in this paper. Based on Lyapunov stability theory and Barbalat's lemma, a new adaptive controller with parameter update law is designed to projectivly synchronize two chaotic systems asymptotically and globally, including two identical exponential-type chaotic systems and two non-identical chaotic systems. Numerical simulations show the effectiveness and the feasibility of the developed methods.