The Global Analysis of Equilibrium Stability in 1-dimensional Systems

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Authors

  • Albert C. J. Luo Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL62026-1805, USA Author

DOI:

https://doi.org/10.5890/JVTSD.2019.09.007

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] Luo, A.C.J. (2012), Continuous Dynamical Systems, HEP/L&H Scientific: Beijing/Glen Carbon.

[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.

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PublishedSeptember 2019

Usage tracking begins September 1, 2026.

History Published

Issue

Vol. 3 No. 3 (2019): Regular Issue

Section

Research Articles

License

Unless an article landing page states a Creative Commons or other article-specific license, the article is published by L&H Scientific Publishing, LLC and all rights are reserved. The article-level license and copyright notice govern access and reuse.

How to Cite

Luo, A. C. J. (2026). The Global Analysis of Equilibrium Stability in 1-dimensional Systems. Journal of Vibration Testing and System Dynamics, 3(3), 347-367. https://doi.org/10.5890/JVTSD.2019.09.007

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