title: Existence of homoclinic connections in continuous piecewise linear systems.
abstract: Numerical methods are often used to put in evidence the existence of global connections in differential systems. The principal reason is that the corresponding analytical proofs are usually very complicated. In this work we give an analytical proof of the existence of a pair of homoclinic connections in a continuous piecewise linear system, which can be considered to be a version of the widely studied Michelson system. Although the computations developed in this proof are specific to the system, the techniques can be extended to other piecewise linear systems.
authors.affiliation: Departamento de Matemática Aplicada II, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, España. vcarmona@us.es
authors.forename: Victoriano
authors.initials: V
authors.lastname: Carmona
authors.forename: Fernando
authors.initials: F
authors.lastname: Fernández-Sánchez
authors.forename: Elisabeth
authors.initials: E
authors.lastname: García-Medina
authors.forename: Antonio E
authors.initials: AE
authors.lastname: Teruel
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D016014:Linear Models; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D010825:Physics / Q000379:methods*