On a closed orbit of some constrained system |
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Authors: | Makoto Hayashi |
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Institution: | (1) Department of Mathematics, College of Science and Technology, Nihon University Funabashi, Chiba 274-8501, Japan |
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Abstract: | We study on what one calls a constrained system of ODEs on
It consists of two ordinary differential equations and an algebraic equation with respect to three unknown functions. We seek closed orbits of such a system. A necessary and sufficient condition for the system to have non-trivial closed orbits is given. Elementary tools such as Lyapunov functions and Poincaré’s index theory are used in the proof of the result. As an application we consider a constrained system associated with a non-constraint system of ODEs called the modified Bonhöffer-van der Pol system. |
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Keywords: | 34C07 34C25 34C26 34D20 |
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