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Title of Journal: Nonlinear Dyn

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Abbravation: Nonlinear Dynamics

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Springer Netherlands

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DOI

10.1007/bf03005472

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1573-269X

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A new study of chaotic behavior and the existence

Authors: ChunYen Ho HsienKeng Chen ZhengMing Ge
Publish Date: 2013/08/01
Volume: 74, Issue: 1-2, Pages: 439-453
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Abstract

In this paper we firstly develop fractionaldegree Hénon maps with increasing and decreasing argument n Yin and Yang are two fundamental opposites in Chinese philosophy Yin represents the moon and is the decreasing negative historical or feminine principle in nature while Yang represents the sun and is the increasing positive contemporary or masculine principle in nature Chaos produced by increasing n is called Yang chaos that by decreasing n Yin chaos respectively The simulation results show that chaos appears via positive Lyapunov exponents bifurcation diagrams and phase portraits In order to examine the existence of chaotic behaviors in fractionaldegree Yin–Yang Hénon maps Feigenbaum’s constants are measured in this paper It is found that the Feigenbaum’s constants in fractionaldegree Yin–Yang Hénon maps are of great precision to the first and second Feigenbaum’s constants A detailed analysis of the chaotic behaviors is also performed for the fractionaldegree Hénon maps with increasing Yang and decreasing Yin argument n

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