We consider gradient vector fields with pulse (smooth and continuous) action defined on a smooth compact manifold. In the course of investigation of the qualitative behavior of integral curves of these vector fields, we prove a criterion for the existence of closed orbits and a condition for their orbital stability.
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Translated from Neliniini Kolyvannya, Vol. 12, No. 1, pp. 134–144, January–March, 2009.
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Sharko, Y.V. Gradient vector fields with pulse action on manifolds. Nonlinear Oscill 12, 137–147 (2009). https://doi.org/10.1007/s11072-009-0067-3
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DOI: https://doi.org/10.1007/s11072-009-0067-3