DU Wen-j
Abstract
An autonomous chaotic system is studied in detail.The local stability of equilibrium is analyzed and the existence of Hopf bifurcation is established.Furthermore,formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived.Finally,a numerical example is given.
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An autonomous chaotic system is studied in detail.The local stability of equilibrium is analyzed and the existence of Hopf bifurcation is established.Furthermore,formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived.Finally,a numerical example is given.
Key concepts: Hopf bifurcation, Bogdanov–Takens bifurcation, Mathematics, Saddle-node bifurcation, Bifurcation diagram, Pitchfork bifurcation, Chaotic, Biological applications of bifurcation theory