在二维多项式系统中限制周期和同临床网络
1Department of Mechanical and Mechatronics Engineering, Southern Illinois University Edwardsville, Edwardsville, Illinois 62026-1805, USA.
Chaos (Woodbury, N.Y.)
|February 27, 2024
概括
这项研究分析了平面多项式动态系统中的平衡性质,确定了同类临床网络中的源,下水槽和的数量. 它还研究了具有极限周期的系统中的和中心,为希尔伯特第16个问题提供了见解.
科学领域:
- 动态系统和混沌理论
- 微分方程 微分方程 微分方程
- 数学分析的数学分析
背景情况:
- 平面多项式动态系统是分析复杂行为的基础.
- 了解平衡属性,如源,水槽和,对于描述系统动态至关重要.
- 同体临床网络在这些系统的定性行为中发挥着重要作用.
研究的目的:
- 研究平面多项式动态系统中平衡的属性.
- 确定自变不变的多项式系统及其同临床网络中的源,下水槽和的数量.
- 分析具有极限循环的交叉无变多项式系统中的和中心的同临床网络.
主要方法:
- 开发和应用定理来确定平衡点的数量 (源,水槽,,中心).
- 使用多项式函数确定第一个积分多元体.
- 同性临床网络的说明性示例,以可视化几何结构.
主要成果:
- 提出了一个定理,该定理确定了自变不变的多项式系统中的源,下水槽和的数量,表明这些网络缺乏中心.
- 另一个定理确定了具有极限周期的交叉无变系统中的和中心的数量,证明没有源和下沉点.
- 讨论了同等度系统的最大平衡点数.
结论:
- 这项研究提供了一种新的方法来理解和确定希尔伯特第16个问题的背景下极限周期.
- 这些发现有助于对平面多项式系统中复杂动态的分类和分析.
- 提出的定理和插图提供了对同性临床网络结构的更深入的了解.
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