The Stability and Bifurcation of the (2m+1)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.2020.06.001

Abstract

In this paper, the global stability and bifurcations of equilibriums in the (2m+1)th -degree polynomial system are discussed for a better understanding of the complexity of bifurcations and stability of equilibriums in such a (2m+1)th-degree polynomial system. The appearing and switching bifurcations for simple and higher-order equilibriums are presented. The broom-teethcomb-appearing, broom-spraying-appearing, and broom-sprinkler-spraying-appearing bifurcations for simple and higher-order equilibriums are presented. The antenna-switching bifurcations for simple and higher-order equilibriums are discussed, and the parallel straw-bundle-switching and ower-bundle-switching bifurcations for simple and higher-order equilibriums are also presented.

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), pp. 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 the stability and bifurcation of equilibriums in nonlinear systems, Journal of Vibration Testing and System Dynamics, 3(2), pp.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), pp. 347-367

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PublishedJune 2020

Usage tracking begins September 1, 2026.

History Published

Issue

Vol. 4 No. 2 (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+1)th-Degree Polynomial Systems. Journal of Vibration Testing and System Dynamics, 4(2), 95-146. https://doi.org/10.5890/JVTSD.2020.06.001

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