In this paper, a new piecewise linear map of the plan and its fractional version deduced from the Lozi map is introduced and analysed. The main attention is paid to the study of fixed points and their stability, cycles of period two and their stability regions and the type of bifurcation that occur in the dynamical behaviours of this map. The routes to chaos and some chaotic attractors that exist in the behaviour of the integer map are discussed. Finally, the chaotic behaviour of the associated proposed fractional map is analysed by means of bifurcations diagrams.

中文翻译：

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一种新的分数分段线性映射：规则和混沌动力学

在本文中，介绍和分析了一种新的规划的分段线性图及其从洛兹图推导出的分数版本。主要关注不动点及其稳定性、周期二周期及其稳定区域的研究，以及在该地图的动力学行为中出现的分岔类型。讨论了混沌路径和存在于整数映射行为中的一些混沌吸引子。最后，通过分岔图分析了相关联的分数映射的混沌行为。