Open AccessA new method for projective synchronization of different fractional order chaotic systems
Author(s) -
Ling Huang,
Nan Ma
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.61.160510
Subject(s) - lyapunov stability , correctness , controller (irrigation) , synchronization (alternating current) , synchronization of chaos , fixed point theorem , chaotic , stability theory , nonlinear system , stability (learning theory) , mathematics , control theory (sociology) , computer science , fractional order system , fractional calculus , mathematical analysis , topology (electrical circuits) , control (management) , algorithm , physics , artificial intelligence , combinatorics , quantum mechanics , machine learning , agronomy , biology
Based on the Lyapunov theory as the breakthrough point, and based on the fractional order system stability theory and properties of fractional nonlinear system, a kind of fractional-order chaotic system is proposed to determine whether the new theorem is stable, and the theory is used for fractional order control and synchronization of chaotic systems, and gives a mathematical proof process to strictly ensure the correctness of the method and general applicability. Then the proposed stability theorem is used to achieve the projective synchronization of fractional Lorenz chaotic system with fractional order chaotic Liu system, as well as the projective synchronization of four-dimensional hyperchaos of fractional order systems of different structures. In the stability theorem solving the fractional balance point and the Lyapunov index are avoided, therefore a control law can be easily selected, and the obtained controller has the advantages of simple structure and wide range of application. Finally, the expected numerical simulation results are achieved, which further proves the correctness and universal applicability of the stability theorem.