Hopf bifurcation analysis of Chen circuit with direct time delay feedback

Direct time delay feedback can make non-chaotic Chencircuit chaotic. The chaotic Chen circuit with direct time delayfeedback possesses rich and complex dynamical behaviours. To reach adeep and clear understanding of the dynamics of such circuitsdescribed by delay differential equations, Hopf bifurcation in thecircuit is analysed using the Hopf bifurcation theory and thecentral manifold theorem in this paper. Bifurcation points andbifurcation directions are derived in detail, which prove to beconsistent with the previous bifurcation diagram. Numericalsimulations and experimental results are given to verify thetheoretical analysis. Hopf bifurcation analysis can explain andpredict the periodical orbit (oscillation) in Chen circuit withdirect time delay feedback. Bifurcation boundaries are derived usingthe Hopf bifurcation analysis, which will be helpful for determiningthe parameters in the stabilisation of the originally chaoticcircuit.