The Stability and Bifurcation of the (2m)th-degree Polynomial 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.2020.03.001

Abstract

In this paper, the global stability and bifurcations of equilibriums in the (2m)th-degree polynomial system are discussed for a better understanding the complexity of bifurcations and stability of equilibriums. The appearing and switching bifurcations for simple equilibriums are presented, and the appearing and switching bifurcations for higherorder equilibriums are discussed as well. The teethcomb-appearing, spraying-appearing, and sprinkler-spraying-appearing bifurcations for simple and higher-order equilibriums are presented. The antennaswitching bifurcations for simple and higher-order equilibriums are discussed and the parallel straw-bundle-switching and flower-bundleswitching bifurcations for simple and higher-order equilibriums are presented as well.

References

[1] Luo, A.C.J. (2019), The stability and bifurcation of low-degree polynomial systems, Journal of Vibration Testing and System Dynamics, 3(4), 403-451.

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

[3] 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.

[4] Luo, A.C.J. (2019), The global analysis of equilibrium stability in 1-dimensional systems, Journal of Vibration Testing and System Dynamics, 3(3), 347-367.

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PublishedMarch 2020

Usage tracking begins September 1, 2026.

History Published

Issue

Vol. 4 No. 1 (2020): Regular Issue

Section

Research Articles

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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 Stability and Bifurcation of the (2m)th-degree Polynomial Systems. Journal of Vibration Testing and System Dynamics, 4(1), 1-42. https://doi.org/10.5890/JVTSD.2020.03.001

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