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A Computable Criterion for the Existence of Connecting Orbits in Autonomous Dynamics |
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| Authors: | Brian A. Coomes Hüseyin Koçak Kenneth J. Palmer |
| Affiliation: | 1.Department of Mathematics,University of Miami,Coral Gables,USA;2.Departments of Mathematics and Computer Science,University of Miami,Coral Gables,USA;3.Department of Financial and Computational Mathematics,Providence University,Taichung,Taiwan;4.Department of Mathematics,National Taiwan University,Taipei,Taiwan |
| Abstract: | A general theorem that guarantees the existence of an orbit connecting two hyperbolic equilibria of a parametrized autonomous differential equation in ({mathbb {R}}^n) near a suitable approximate connecting orbit given the invertibility of a certain explicitly given matrix is proved. Numerical implementation of the theorem is described using five examples including two Sil’nikov saddle-focus homoclinic orbits and a Sil’nikov saddle-focus heteroclinic cycle. |
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