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Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland


C. Steve Suh (editor)

Texas A&M University, USA


Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China


The Global Analysis of Equilibrium Stability in 1-dimensional Systems

Journal of Vcibration Testing and System Dynamics 3(3) (2019) 347--367 | DOI:10.5890/JVTSD.2019.09.007

Albert C. J. Luo

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

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In this paper, a global analysis of equilibrium stability in 1-dimensional nonlinear dynamical systems is presented. The classification of dynamical systems is given first, and infinite-equilibrium systems are defined. The 1-dimensional dynamical systems with a single equilibrium are discussed. The 1-dimensional dynamical systems with two and three equilibriums are discussed. Simple and higher-order equilibriums in 1-dimensional dynamical systems are analyzed, and a higherorder equilibrium is an equilibrium with higher-order singularity. The flows of equilibriums in 1-dimensional systems in phase space are illustrated for a better understanding of the global stability of equilibriums in 1-dimensional dynamical systems.


  1. [1]  Luo, A.C.J. (2012), Continuous Dynamical Systems, HEP/L&H Scientific: Beijing/Glen Carbon.
  2. [2]  Luo, A.C.J. (2019), On stability and bifurcation of equilibriums in nonlinear systems, Journal of Vibration Testing and System Dynamics, 3(2), 147-232.