中心或极限环：重整化群的探索
Center or Limit Cycle: Renormalization Group as a Probe
摘要：
基于我们对二维自治系统、强迫非自治系统和时滞系统的研究，我们提出了一个统一的方法--利用重整化群理论--来寻找跨学科出现的大量非线性动力系统的周期解的存在性。该技术将被证明有一个非平凡的能力，分类的解决方案到极限环和周期轨道周围的中心。此外，该方法具有一定的优势，在分析中心的线性稳定性分析。
英文摘要：
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic solutions in a plethora of nonlinear dynamical systems appearing across disciplines. The technique will be shown to have a non-trivial ability of classifying the solutions into limit cycles and periodic orbits surrounding a center. Moreover, the methodology has a definite advantage over linear stability analysis in analyzing centers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
