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

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Document pages: 19 pages

Abstract: In the present paper, a custom algorithm based on the method of orthogonal collocation onfinite elements is presented and used for the location of global homoclinicpoint-to-point asymptotic connecting orbits. This kind of global bifurcationoccurs in a large variety of problems in Applied Sciences, being associated tospecific, significant physical aspects of the problem under consideration. Inorder to confront the difficulties faced when the location of such orbits isattempted, high order boundary conditions are constructed through scale orderapproximations, and used instead of the more common first order ones. Theeffectiveness of the implemented algorithm is justified by means of thespecific applications and the figures presented.

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