四川师范大学学报（自然科学版）2025，Vol.48Issue(4)：466-476,11.DOI:10.3969/j.issn.1001-8395.2025.04.004
几何奇异摄动理论及其应用
Geometric Singular Perturbation Theory and Its Applications
摘要
Abstract
Singular perturbation theory was initiated from engineering and its applications.The research methods to studying their dynamics are nonstandard analysis and asymptotic expansion method in past.With development of geometric theory for dynamical sys-tems,the researches formulated a series of geometric theories.This theory is based on Fenichel's normally hyperbolic invariant mani-fold theory,then there appear the theories and techniques to handling turning point.This paper summarizes Fenichel's three invariant manifold theories,together with jump and canard point theories,entry and exit function theory on turning point,and the exchange lem-ma dealing with the evolution of the flow from center stable manifold to center unstable manifold.Some applications of these theories to biological mathematical models and so on are also presented.关键词
奇异摄动系统/Fenichel不变流形理论/折点和转向点理论/交换引理/生物数学Key words
singularly perturbed system/Fenichel invariant manifold theory/fold and turning point theory/exchange lemma/bio-logical mathematics分类
数学引用本文复制引用
张祥..几何奇异摄动理论及其应用[J].四川师范大学学报（自然科学版）,2025,48(4):466-476,11.基金项目
国家自然科学基金(12471169、12071284和12161131001) （12471169、12071284和12161131001）
