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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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Abstract

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.

References

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.