In this paper, we study the limit cycle of a nonlinear conveyor belt system by utilizing the perturbation incremental method. We first divide the system into two subclasses. On account of the former is heteroclinic orbit and the latter is not, there are some differences in the process of employing this method. Next two steps are introduced, the perturbation part provides the zero-order perturbation solution and takes it as the initial value of the incremental part, and in the incremental part, the corresponding limit cycle is obtained by controlling the value of the parameter \(\lambda \). Under this circumstance, approximate analytical expressions of limit cycles of those classes are found. Then, numerical simulations are presented to prove the effectiveness of the results by comparison with numerical integration using the fourth-order Runge–Kutta method. Finally, some conclusions and expectations are given.

在本文中，我们利用扰动增量法研究了非线性传送带系统的极限环。我们首先将系统分为两个子类。由于前者是异宿轨道而后者不是，因此在采用这种方法的过程中存在一些差异。接下来介绍两步，扰动部分给出零阶扰动解并作为增量部分的初始值，在增量部分通过控制参数\(\拉姆达 \). 在这种情况下，找到了这些类极限环的近似解析表达式。然后，通过与使用四阶 Runge-Kutta 方法的数值积分进行比较，数值模拟证明了结果的有效性。最后，给出了一些结论和期望。