精品文档---下载后可任意编辑两类多项式微分系统的极限环讨论的开题报告【摘要】本文着重讨论了两类多项式微分系统的极限环问题，分别为周期功率微分系统和正幂次微分系统。首先，详细介绍了这两种微分系统的基本概念和数学模型，并分析了它们在动力学系统中的重要性。然后，以周期功率微分系统为例，运用 Takens-Bogdanov 和 Hopf 定理证明了该系统的存在极限环的特性，并给出了极限环的具体形态和分析。最后，以正幂次微分系统为例，运用 Lyapunov 方法和 Poincaré-Bendixon定理证明了该系统的存在无限多个极限环的特性，并利用数值模拟验证了理论结果。【关键词】多项式微分系统；周期功率微分系统；正幂次微分系统；极限环；Takens-Bogdanov 定理；Hopf 定理；Lyapunov 方法；Poincaré-Bendixon 定理【Abstract】This paper focuses on the study of limit cycles for two types of polynomial differential systems, namely the periodic power differential system and the positive power differential system. Firstly, the basic concepts and mathematical models of these two differential systems are introduced in detail, and their importance in dynamical systems is analyzed. Then, taking the periodic power differential system as an example, the existence of limit cycles and their specific form and analysis are proved using the Takens-Bogdanov and Hopf theorems. Finally, taking the positive power differential system as an example, the existence of infinitely many limit cycles and their theoretical results are verified by numerical simulations using the Lyapunov method and Poincaré-Bendixon theorem.【Keywords】polynomial differential system; periodic power differential system; positive power differential system; limit cycle; Takens-Bogdanov theorem; Hopf theorem; Lyapunov method; Poincaré-Bendixon theorem
