TITLE:
High Order Boundary Conditions Technique for the Computation of Global Homoclinic Bifurcation
AUTHORS:
Panagiotis S. Douris, Michail P. Markakis
KEYWORDS:
Homoclinic Connections, Orthogonal Collocation on Finite Elements, Limit Cycles
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.3,
March
23,
2018
ABSTRACT: 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.