A Class of One-dimensional Chaotic Quadratic Curves

Wan-bo YU


The paper studies the chaotic characteristics of a class of quadratic functions. In order to facilitate research, the Bézier control points are used to stretch the Logistic curve toward left-right or up-down. This family of quadratic curves are Li-Yorke chaos when certain conditions are met, it has been proved with Marotto snap-back-repeller’s theorem. In addition to this main results, the parameter points which are able to generate chaos are shown on the plane. From an application point of view, we will get more chaotic curves by moving the control points at both ends, that the chaotic curves can be used to generate chaotic sequences.


Chaos, Dynamical systems, Quadratic curves


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