Open AccessChaos in fractional-order Liu system and a fractional-order unified system and the synchronization between them
Author(s) -
Zhang Cheng-fen,
Jinfeng Gao,
Xu Lei
Publication year - 2007
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.56.5124
Subject(s) - order (exchange) , chaos (operating system) , fractional order system , synchronization (alternating current) , synchronization of chaos , lyapunov exponent , chaotic , chaotic systems , mathematics , control of chaos , fractional calculus , computer science , lorenz system , control theory (sociology) , statistical physics , physics , control (management) , topology (electrical circuits) , artificial intelligence , computer security , finance , combinatorics , economics
This paper studies the chaotic behaviors of the fractional-order Liu system and the fractional-order unified system which were presented several years ago. It is found that chaos exists in the both systems with order less than three and the lowest order to have chaos is 0.3. The calculation results of the maximum Lyapunov exponents when the system is chaotic illustrate the existence of chaos. Chaos synchronization between fractional-order Liu system, fractional-order Lorenz system and fractional-order Lü sytem is realized by employing active control technique. Theoretieal analysis and numerical simulations demonstrate the effectiveness of the proposed method.