In this paper, we investigated the unstable periodic orbits of a nonlinear chaotic generalized Lorenz-type system. By means of the variational method, appropriate symbolic dynamics are put forward, and the homotopy evolution approach, which can be used in the initialization of the cycle search, is introduced. Fourteen short unstable periodic orbits with different topological lengths, under specific parameter values, are calculated. We also explored the continuous deformation for part of the orbits while changing the parameter values , which provides a new approach to observe various bifurcations. The scale transformation of the generalized Lorenz-type system leads to a single parameter system known as the diffusionless Lorenz equations. By systematically calculating the periodic orbits in the diffusionless Lorenz equations, our research shows the efficiency of this topological classification method for the periodic solutions in the variants of a classical Lorenz system.

中文翻译：

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广义Lorenz型系统中的不稳定周期轨道分析。

在本文中，我们研究了非线性混沌广义Lorenz型系统的不稳定周期轨道。通过变分方法，提出了合适的符号动力学，并介绍了可用于循环搜索初始化的同伦进化方法。在特定参数值下，计算了十四个具有不同拓扑长度的短不稳定周期轨道。我们还探索了改变参数值时部分轨道的连续变形，这为观察各种分叉提供了一种新方法。广义Lorenz型系统的尺度变换导致了一个称为无扩散Lorenz方程的单参数系统。通过系统地计算无扩散Lorenz方程中的周期轨道，