Abstract
In this Chapter, basic concepts of nonlinear dynamical systems will be presented as a review material. Local theory, global theory and bifurcation theory of nonlinear dynamical systems will be discussed. The stability switching and bifurcation on specific eigenvectors of the linearized system at equilibrium will be presented. The higher singularity and stability for nonlinear systems on the specific eigenvectors will be developed. In addition, a periodically excited Duffing oscillator with cubic damping and constant force will be discussed as an application. The stability of approximate periodic solutions of such a Duffing oscillator will be discussed.
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