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The algorithm of singular point quantities for an equilibrium of three-dimensional dynamics system is studied. The explicit algebraic equivalent relation between singular point quantities and Liapunov constants on center manifold is rigorously proved. As an example, the calculation of singular point quantities of the Lü system is applied to illustrate the advantage in investigating Hopf bifurcation of threedimensional system. © 2012 Wang and Huang.

The equivalence between singular point quantities and Liapunov constants on center manifold