Abstract
We study a bifurcation from the zero solution of the differential equation ẍ + xp/q = 0, where p > q > 1 are odd coprime numbers, under periodic (in particular, time-invariant) perturbations depending on a small positive parameter ε. The motion separation method is used to derive the bifurcation equation. To each positive root of this equation, there corresponds an invariant two-dimensional torus (a closed trajectory in the time-invariant case) shrinking to the equilibrium position x = 0 as ε → 0. The proofs use methods of the Krylov-Bogolyubov theory to study time-periodic perturbations and the implicit function theorem in the case of time-invari ant perturbations.
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Russian Text © The Author(s), 2019, published in Differentsial’nye Uravneniya, 2019, Vol. 55, No. 6, pp. 769–773.
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Bibikov, Y.N., Bukaty, V.R. Bifurcation of an Oscillatory Mode under a Periodic Perturbation of a Special Oscillator. Diff Equat 55, 753–757 (2019). https://doi.org/10.1134/S001226611906003X
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DOI: https://doi.org/10.1134/S001226611906003X