奇异摄动系统的周期振荡  

Periodic Oscillations in Singular Perturbation Systems

作　　者：赵亮[1,2] 沈建和[1] ZHAO Liang;SHEN Jianhe(School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China;School of Information and Statistics,Guangxi University of Finance and Economics,Nanning 530003,China)

机构地区：[1]福建师范大学数学与统计学院,福建福州350117 [2]广西财经学院信息与统计学院,广西南宁530003

出　　处：《福建师范大学学报（自然科学版）》2022年第4期11-19,共9页Journal of Fujian Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11771082);广西自然科学基金资助项目(2022GXNSFBA035466);广西高校中青年教师科研基础能力提升项目(2021KY0653)。

摘　　要：综述了多尺度奇异摄动系统复杂周期振荡的存在形式、产生机制和研究现状.特别地,对三尺度三维奇异摄动系统的混合模式振荡(MMOs)的局部小振荡的产生机制及其相互作用进行了详细的介绍.同时,以一类三尺度食物链模型为例,对有关的概念等进行了具体的说明.This paper reviews the existing forms,generation mechanisms and research advances of complex periodic oscillationsin in multi-scale singular perturbation systems.In particular,the generation mechanisms of locally small amplitude oscillation for the mixed-mode oscillations(MMOs)as well as their interactions with three-timescale and three-dimensional singular perturbation systems are introduced in detail.Also this paper provides a three-timescale food chain model as an example to illustrate some related concepts.

关 键 词：三尺度 奇异摄动 混合模式振荡 小振幅振荡 

分 类 号：O174.52[理学—数学]