The work in this paper consists of two parts. The one is modelling. After a method of classification for three dimensional (3D) autonomous chaotic systems and a concept of mixed Lorenz system are introduced, a mixed Lorenz system with a damped term is presented. The other is the analysis for dynamical properties of this model. First, its local stability and bifurcation in its parameter space are in detail considered. Then, the existence of its homoclinic and heteroclinic orbits, and the existence of singularly degenerate heteroclinic cycles, are studied by rigorous theoretical analysis. Finally, by using the Poincaré compactification for polynomial vector fields in R 3 ${\mathbb{R}}^{3}$ , a global analysis of this system near and at infinity is presented, including the complete description of its dynamics on the sphere near and at infinity. Simulations corroborate corresponding theoretical results. In particular, a possibly new mechanism for the creation of chaotic attractors is proposed. Some different structure types of chaotic attractors are correspondingly and numerically found.

中文翻译：

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具有阻尼项的3D混合Lorenz系统动力学的建模和分析

本文的工作包括两部分。一个是建模。在介绍了三维（3D）自治混沌系统的分类方法和混合洛伦兹系统的概念之后，提出了具有阻尼项的混合洛伦兹系统。另一个是对该模型的动力学特性的分析。首先，详细考虑了其在参数空间中的局部稳定性和分叉性。然后，通过严格的理论分析，研究了其同宿和异宿轨道的存在以及奇异退化的异宿循环的存在。最后，通过对R 3 $ {\ mathbb {R}} ^ {3} $中的多项式矢量场进行Poincaré压缩，给出了对该系统在无限远处和无限处的全局分析，包括其在动力学上的完整描述。球体在无穷远处。仿真证实了相应的理论结果。特别地，提出了一种可能的用于创建混沌吸引子的新机制。相应地并在数值上发现了一些不同类型的混沌吸引子。