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arXiv · 2308.08835

Stability range of parameters at fixed points for a class of complex dynamics

Zhen-Hua Feng·Hai-Bo Sang·B. S. Xie
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Abstract

We study the parameters range for the fixed point of a class of complex dynamics with the rational fractional function as $R_{n,a,c}(z)=z^n+\frac{a}{z^n}+c$, where $n=1,2,3,4$ is specified, $a$ and $c$ are two complex parameters. The relationship between two parameters, $a$ and $c$, is obtained at the fixed point. Moreover the explicit expression of the parameter $a$ and $c$ in terms of $\lambda$ is derived, where $\lambda$ is the derivative function at fixed point. The parameter regimes for the stability of the fixed point are presented numerically for some typical different cases.

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Zhen-Hua Feng, Hai-Bo Sang, B. S. Xie. 2023-08-17. Stability range of parameters at fixed points for a class of complex dynamics. https://arxiv.org/abs/2308.08835

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