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Journal of Vcibration Testing and System Dynamics 3(4) (2019) 403--451 | DOI:10.5890/JVTSD.2019.12.003

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 stability and bifurcation of equilibriums in low-degree polynomial systems are discussed. Appearing and switching bifurcations of simple and higher order equilibriums are discussed, and such bifurcations of equilibriums are not only for simple equilibriums but for higher-order equilibriums. The 3rd-order sink and source bifurcations for simple equilibriums are presented. The 3rd-order sink and source switching bifurcations for saddle and nodes are discovered, and the 4th-order upper-saddle and lower-saddle switching and appearing bifurcations are obtained for two 2nd-order upper-saddles and two 2nd-order lower-saddles, respectively. Graphical illustrations of global stability and bifurcations are presented.

References

1. [1]	Luo, A.C.J., 2012, Continuous Dynamical System, HEP/L&H Scientific: Beijing/Glen Carbon.

2. [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.

3. [3]	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.