论文标题
限制循环和具有平衡点线的连续系统
Limit cycles and Integrability of a continuous system with a line of equilibrium points
论文作者
论文摘要
我们专注于三维的混乱差分系统，包括绝对项和平衡点。在以下系统中描述的该系统具有电子组件中的实现。本文的第一个目的是为存在从位于坐标原点的零平衡点分叉的极限周期提供足够的条件。第二个目的是研究每个差分系统的整合性，一个系统以半空间y定义，另一个定义为半空间y。我们证明，这两个系统对于任何值的a，b和c的值都没有多项式，有理或darboux的第一积分。此外，我们提供了正式的系列和这些系统的分析第一组成部分。我们还对Darboux多项式和指数因素进行了分类。
We focus on a chaotic differential system in 3-dimension, including an absolute term and a line of equilibrium points. Which describes in the following This system has an implementation in electronic components. The first purpose of this paper is to provide sufficient conditions for the existence of a limit cycle bifurcating from the zeroHopf equilibrium point located at the origin of the coordinates. The second aim is to study the integrability of each differential system, one defined in half-space y and the other in half-space y. We prove that these two systems have no polynomial, rational, or Darboux first integrals for any value of a, b, and c. Furthermore, we provide a formal series and an analytic first integral of these systems. We also classify Darboux polynomials and exponential factors.
