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

Journal of Vcibration Testing and System Dynamics 4(1) (2020) 1--42 | DOI:10.5890/JVTSD.2020.03.001

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)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.