Abstract

In this chapter, basic concepts of nonlinear dynamical systems are introduced. A local theory of equilibrium stability for nonlinear dynamical systems is discussed. The spiral stability of equilibriums in nonlinear dynamical systems is presented through the Fourier series base. The higher order singularity and stability for nonlinear systems on the specific eigenvectors are developed. The Lyapunov function stability is briefly discussed, and the extended Lyapunov theory for equilibrium stability is also presented.

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