High Order Boundary Conditions Technique for the Computation of Global Homoclinic Bifurcation - Journal of Applied Mathematics and Physics

JAMP > Vol.6 No.3, March 2018

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

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DOI: 10.4236/jamp.2018.63049 705 Downloads 1,380 Views Citations

Author(s)

Panagiotis S. Douris, Michail P. Markakis^*

Affiliation(s)

Department of Electrical & Computer Engineering, University of Patras, Patras, Greece.

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.

KEYWORDS

Homoclinic Connections, Orthogonal Collocation on Finite Elements, Limit Cycles

Share and Cite:

Douris, P. and Markakis, M. (2018) High Order Boundary Conditions Technique for the Computation of Global Homoclinic Bifurcation. Journal of Applied Mathematics and Physics, 6, 554-572. doi: 10.4236/jamp.2018.63049.

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