Open AccessDetermining the controllable conditions for time-delayed feedback chaos control
Author(s) -
Xiaoming Zhang,
Jianhua Peng,
Guanrong Chen
Publication year - 2004
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.53.2864
Subject(s) - hopf bifurcation , control theory (sociology) , chaotic , chaos (operating system) , feedback control , control of chaos , chaotic systems , stability (learning theory) , periodic orbits , bifurcation , period doubling bifurcation , control (management) , physics , mathematics , synchronization of chaos , computer science , mathematical analysis , nonlinear system , control engineering , quantum mechanics , computer security , artificial intelligence , machine learning , engineering
Based on Hopf bifurcation theory and methods in time-delayed systems, we ana lytically determine some general conditions of time-delayed feedback control of three-dimensional autonomous chaotic systems. With this method, a criterion for the stability of periodic solution under control and for the direction of Hopf b ifurcation is derived theoretically studied. Applying the method to the control of some three-dimensional autonomous chaotic systems, we can analytically find the cont rollable parameter in this region. Choosing parameters in it, we can successfull y stabilize chaotic orbits to periodic states.