Abstract.
We study on what one calls a constrained system of ODEs on \(\mathbb{R}^3. \) 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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Hayashi, M. On a closed orbit of some constrained system. Nonlinear differ. equ. appl. 12, 61–70 (2005). https://doi.org/10.1007/s00030-004-2026-0
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DOI: https://doi.org/10.1007/s00030-004-2026-0