Open AccessDynamic behavior and chaos synchronization of a simple nonlinear time-delayed system
Author(s) -
JiangWen Xiao,
Jufang Chen,
Jianhua Peng
Publication year - 2013
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.62.170507
Subject(s) - period doubling bifurcation , bifurcation , synchronization (alternating current) , control theory (sociology) , bifurcation diagram , nonlinear system , hopf bifurcation , chaotic , simple (philosophy) , computer simulation , trajectory , control of chaos , biological applications of bifurcation theory , computer science , synchronization of chaos , physics , mathematics , mechanics , topology (electrical circuits) , control (management) , philosophy , epistemology , quantum mechanics , combinatorics , artificial intelligence , astronomy
Hopf bifurcation and chaotic properties of a simple second order time-delayed system, which includes bifrucation point, bifurcation direction and the stability of bifrucating periodic solutions, are analyzed. We obtain analytically the phase trajectory equations when the delay degenerates. Furthermore, through bifurcation diagram drawn by means of numerical simulation, the route from period-doubling bifurcation to chaos is reaveled; using single linearly combinating signals and the feedback control method, we achieve partial synchronization of the system. Combining the active-passive method with the linear feedback method, we have realized complete synchronization. In addition, we have designed and built an electronic experimental line, from which the same result as the theoretical analysis or numerical results are obtained.