Abstract
In this chapter, a global analysis of equilibrium stability in 1-dimensional nonlinear dynamical systems is presented. The classification of dynamical systems is given first, and infinite-equilibrium systems are defined. The 1-dimensional dynamical systems with single equilibrium are discussed first. The 1-dimensional dynamical systems with two and three equilibriums are discussed. Simple equilibriums and higher order equilibriums in 1-dimensional dynamical systems are analyzed, and herein a higher order equilibrium is an equilibrium with higher order singularity. The separatrix flow of equilibriums in 1-dimensional systems in phase space is illustrated for a better understanding of the global stability of equilibriums in 1-dimensional dynamical systems.
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