Chaotic maps with higher chaotic complexity are urgently needed in many application scenarios. This paper proposes a chaotification model based on sine and cosecant functions (CMSC) to improve the dynamic properties of existing chaotic maps. CMSC can generate a new map with higher chaotic complexity by using the existing one-dimensional (1D) chaotic map as a seed map. To discuss the performance of CMSC, the chaos properties of CMSC are analyzed based on the mathematical definition of the Lyapunov exponent (LE). Then, three new maps are generated by applying three classical 1D chaotic maps to CMSC respectively, and the dynamic behaviors of the new maps are analyzed in terms of fixed point, bifurcation diagram, sample entropy (SE), etc. The results of the analysis demonstrate that the new maps have a larger chaotic region and excellent chaotic characteristics.

中文翻译：

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基于正弦余割函数的混沌强化模型

许多应用场景迫切需要混沌复杂度更高的混沌映射。本文提出了一种基于正弦余割函数（CMSC）的混沌模型来改善现有混沌映射的动态特性。CMSC 可以使用现有的一维（1D）混沌图作为种子图，生成具有更高混沌复杂度的新图。为了讨论 CMSC 的性能，基于 Lyapunov 指数 (LE) 的数学定义分析了 CMSC 的混沌特性。然后，分别将三个经典的一维混沌映射应用于CMSC，生成三个新映射，并从不动点、分岔图、样本熵（SE）等方面分析新映射的动态行为。