The Stability and Bifurcation of the (2m+1)th-Degree Polynomial Systems

Albert C J Luo

Journal of Vibration Testing and System Dynamics

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

Xianguo Tuo (editor)

The Stability and Bifurcation of the (2m+1)th-Degree Polynomial Systems

Journal of Vcibration Testing and System Dynamics 4(2) (2020) 95--146 | DOI:10.5890/JVTSD.2020.06.001

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, 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