A New Class of Two-Dimensional Chaotic Maps with Closed Curve Fixed Points
A New Class of Two-Dimensional Chaotic Maps with Closed Curve Fixed Points
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一类新的闭曲线不动点二维混沌映射
DOI：
10.1142/s0218127419500949
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发表时间：
2019-06-01
影响因子：
2.2
通讯作者：
Zhang, Liping
中科院分区：
文献类型：
--
作者：
Jiang, Haibo;Liu, Yang;Zhang, Liping
构造了一类新的具有闭曲线不动点的二维映射。首先，通过引入非线性函数建立了这些映射的数学模型。通过选择适当的非线性函数参数，给出了形成闭曲线的不同类型的不动点。研究了这些不动点的稳定性，证明了这些不动点都是非双曲的。然后利用计算机搜索程序对这些映射中的混沌吸引子进行了探索，并给出了几种不动点形成不同形状闭曲线的简单映射。利用相盆图、李雅普诺夫指数和分岔图研究了这些映射的复杂动力学行为。
This paper constructs a new class of two-dimensional maps with closed curve fixed points. Firstly, the mathematical model of these maps is formulated by introducing a nonlinear function. Different types of fixed points which form a closed curve are shown by choosing proper parameters of the nonlinear function. The stabilities of these fixed points are studied to show that these fixed points are all nonhyperbolic. Then a computer search program is employed to explore the chaotic attractors in these maps, and several simple maps whose fixed points form different shapes of closed curves are presented. Complex dynamical behaviors of these maps are investigated by using the phase-basin portrait, Lyapunov exponents, and bifurcation diagrams.