Open AccessHopf bifurcation control of the Rössler system based on Washout filter controller
Author(s) -
Zhaoming Wu,
Li Sun
Publication year - 2011
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.60.050504
Subject(s) - control theory (sociology) , hopf bifurcation , filter (signal processing) , controller (irrigation) , position (finance) , bifurcation , nonlinear system , amplitude , bifurcation diagram , mathematics , mathematical analysis , physics , computer science , control (management) , optics , finance , quantum mechanics , artificial intelligence , agronomy , economics , computer vision , biology
The Washout filter is adopted to control Hopf bifurcation in Rössler system. The effect of its parameters on the position of bifurcation point, the bifurcation type, and the amplitude of periodic solution is discussed in detail. Based on Routh criterion, the stability region in parameter space is found out firstly. Then the influence of the filter’s time constant and the linear gain on the location of bifurcation point is analyzed. By using the Direct Normal Form method, the normal form of the controlled Rössler system is deduced and the coefficient of resonant term is expressed as a function of the nonlinear gain. It is revealed that, by changing the sign and the absolute value of the real part of the coefficient, the nonlinear gain can modify the periodic solution’s amplitude and Hopf bifurcation type. All the results obtained are verified by numerical simulation.