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Journal of Vcibration Testing and System Dynamics 3(2) (2019) 147--232 | DOI:10.5890/JVTSD.2019.06.004

Albert C. J. Luo

Department of Mechanical Engineering, Southern Illinois University Edwardsville, Edwardsville, IL62026-1805, USA

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Abstract

In this paper, a local theory for stability and bifurcation of equilibriums for nonlinear dynamical systems is presented. The stability and bifurcation on specific eigenvectors of the linearized system at equilibrium is discussed. The higher-order singularity and stability for nonlinear systems on the specic eigenvectors are developed. The Hopf bifurcation based on the transformation of the Fourier series base is also discussed. The stability and bifurcation of equilibriums in low-dimensional dynamical systems is discussed for a better understanding of stability and bifurcation theory. The Lyapunov function stability is briey discussed, and the extended Lyapunov stability theory is presented.

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