Analysis of a Shil’nikov Type Homoclinic Bifurcation

作     者：Yan Cong XU Xing Bo LIU 

作者机构：Department of Mathematics Hangzhou Normal University Hangzhou 310036 P. R. China Department of Mathematics Shanghai Key Laboratory of PMMP East China Normal University Shanghai 200241 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2018年第34卷第5期

页      面：901-910页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 070104[理学-应用数学] 071101[理学-系统理论] 0701[理学-数学] 

基　　金：Supported by National NSF(Grant Nos.11371140,11671114) Shanghai Key Laboratory of PMMP 

主　　题：Homoclinic bifurcation Hopf bifurcation Poincare map 

摘      要：The bifurcation associated with a homoclinic orbit to saddle-focus including a pair of pure imaginary eigenvalues is investigated by using related homoclinie bifurcation theory. It is proved that, in a neighborhood of the homoclinic bifurcation value, there are countably infinite saddle-node bifurcation values, period-doubling bifurcation values and double-pulse homoclinic bifurcation values. Also, accompanied by the Hopf bifurcation, the existence of certain homoclinie connections to the periodic orbit is proved.