Abstract
In this chapter, the hyperbolic bifurcations of equilibriums on the eigenvectors in nonlinear dynamical systems are discussed, and the Hopf bifurcation of an equilibrium on a specific eigenvector plane is presented. Based on the Fourier series base, the transformation for the spiral stability is introduced for the Hopf bifurcation of equilibriums. The Hopf bifurcation of equilibriums in the second-order nonlinear dynamical systems is discussed from the Fourier series transformation.
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