High Order Boundary Conditions Technique for the Computation of Global Homoclinic Bifurcation

• 作者: Michail P. Markakis Panagiotis S. Douris
• 来源期刊: 应用数学与应用物理(英文)
• 学科: 数学
• 关键词: HOMOCLINIC Connections ORTHOGONAL COLLOCATION on Finite Elements Limit Cycles
• 年，卷（期）: 2018,（3）
• 页码范围: 554-572
• 页数: 19页
• 分类号: O1

摘要

In the present paper, a custom algorithm based on the method of orthogonal collocation on finite elements is presented and used for the location of global homoclinic point-to-point asymptotic connecting orbits. This kind of global bifurcation occurs in a large variety of problems in Applied Sciences, being associated to specific, significant physical aspects of the problem under consideration. In order to confront the difficulties faced when the location of such orbits is attempted, high order boundary conditions are constructed through scale order approximations, and used instead of the more common first order ones. The effectiveness of the implemented algorithm is justified by means of the specific applications and the figures presented.