Hopf bifurcation analysis of Chen circuit with direct time delay feedback |
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Authors: | Ren Hai-Peng Li Wen-Chao and Liu Ding |
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Institution: | School of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048, China |
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Abstract: | Direct time delay feedback can make non-chaotic Chen
circuit chaotic. The chaotic Chen circuit with direct time delay
feedback possesses rich and complex dynamical behaviours. To reach a
deep and clear understanding of the dynamics of such circuits
described by delay differential equations, Hopf bifurcation in the
circuit is analysed using the Hopf bifurcation theory and the
central manifold theorem in this paper. Bifurcation points and
bifurcation directions are derived in detail, which prove to be
consistent with the previous bifurcation diagram. Numerical
simulations and experimental results are given to verify the
theoretical analysis. Hopf bifurcation analysis can explain and
predict the periodical orbit (oscillation) in Chen circuit with
direct time delay feedback. Bifurcation boundaries are derived using
the Hopf bifurcation analysis, which will be helpful for determining
the parameters in the stabilisation of the originally chaotic
circuit. |
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Keywords: | direct time delay feedback bifurcation diagram Hopf
bifurcation bifurcation boundary |
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