Abstract
In this Chapter, as in Luo (2019, 2020), a global analysis of fixed-point stability in 1-dimensional nonlinear discrete systems is presented. The classification of discrete systems is discussed first, and infinite-fixed-point discrete systems are presented. The 1-dimensional discrete systems with a single fixed-point are discussed first. The 1-dimensional discrete systems with two and three fixed-points are discussed. Simple fixed-points and higher-order fixed-points in 1-dimensional discrete systems are analyzed, and herein a higher-order fixed-point is a fixed-point with higher-order singularity. The discrete flow of fixed-points in 1-dimensional systems in alike phase space are illustrated for a better understanding of the global stability of fixed-points in 1-dimensional discrete systems.
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