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.
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