分段光滑系统中同宿环附近的极限环分支（英文）  

Limit Cycle Bifurcations Near a Homoclinic Loopin Piecewise Smooth Systems

作　　者：卫丽君[1] 梁峰[1] 鲁世平[1,2] 

机构地区：[1]安徽师范大学数学与计算机科学学院,安徽芜湖241000 [2]南京信息工程大学数学与统计学院,江苏南京210044

出　　处：《应用数学》2014年第2期283-291,共9页Mathematica Applicata

基　　金：the Natural Science Foundation of Anhui Province(1308085MA08);the Doctor Program Foundation(2012)of Anhui Normal University;the NNSF of China(11271197);the key NSF of Education Ministry of China(207047)

摘　　要：在对机械、工程、生物等的实际应用中,非光滑动力系统的理论研究已经被广泛应用.本文将同宿分支在光滑动力系统中的研究结果推广到分段光滑动力系统中.假设平面分段光滑动力系统中存在一个含有双曲鞍点的分片光滑的同宿环,并且在同宿环内有一族闭轨.通过计算一阶Melnikov函数的展开式系数得出同宿环在扰动过后产生的极限环的个数.Non-smooth dynamical systems have been widely used in mechanics, engineering and biology fields. Here,a result on bifurcations of limit cycles is extended from smooth dynamical systems to piecewise smooth dynamical systems. For it, suppose a planar piecewise smooth Hamiltonian system has a piecewise homoclinic loop with a hyperbolic saddle,and assume that there is a family of periodic orbits inside the loop. Under perturbations we first give the expansion of the first Melnikov function near the loop. Then by using the first coefficients in the expansion, we study the number of limit cycles bifurcating from the homoclinic loop.

关 键 词：MELNIKOV函数 极限环分支 同宿环 分段光滑系统 近哈密顿系统 

分 类 号：O175.1[理学—数学]