In this paper a nonlinear planar autonomous system having a limit cycle of period T which is perturbed by a small parameter nonautonomous T-periodic nonlinear term is considered. By using the topological index of the equilibrium points of the unperturbed system and a geometric condition on the perturbation, similar to the condition of the guiding function method as introduced by M. A. Krasnoselskii - A. I. Perov, the existence of T-periodic solutions of the perturbed system close as we like to the limit cycle of the autonomous system is proved. Copyright © 2004 IFAC
Kamenski, M., Makarenkov, O., Nistri, P. (2004). Small periodic perturbations of autonomous self-oscillating planar systems. In IFAC Workshop on "Periodic Control Systems" (pp.363-366). Laxenburg : IFAC Secretariat [10.1016/S1474-6670(17)31495-7].
Small periodic perturbations of autonomous self-oscillating planar systems
NISTRI, PAOLO
2004-01-01
Abstract
In this paper a nonlinear planar autonomous system having a limit cycle of period T which is perturbed by a small parameter nonautonomous T-periodic nonlinear term is considered. By using the topological index of the equilibrium points of the unperturbed system and a geometric condition on the perturbation, similar to the condition of the guiding function method as introduced by M. A. Krasnoselskii - A. I. Perov, the existence of T-periodic solutions of the perturbed system close as we like to the limit cycle of the autonomous system is proved. Copyright © 2004 IFAC
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https://hdl.handle.net/11365/35404
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