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- W2023189967 abstract "Abstract. We study singularly perturbed scalar and planar differential equations with lin-ear parts independent of time. The associated autonomous equations undergo a bifurcationof equilibria in the scalar case and the Hopf bifurcation in the case of planar systems at abifurcation point where the zero equilibrium loses stability. We suggest natural sufficient con-ditions for the phenomenon of delayed loss of stability for the singularly perturbed equationsand estimate the asymptotic delay. Bifurcation points, stability of the zero equilibrium, andthe asymptotic delay are determined by superlinear terms in the expansions of the right-handsides of the associated and singularly perturbed equations.Keywords: Singular perturbation, delayed loss of stability, periodic solution, Hopf bifurcation AMS subject classification: 34D15, 37G15 1. Introduction We consider singularly perturbed equations dxd? = g ( ?;x ) (1 : 1)and study the asymptotic behavior of solutions of the Cauchy problem for small valuesof the parameter" @default.
- W2023189967 created "2016-06-24" @default.
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- W2023189967 date "2003-01-01" @default.
- W2023189967 modified "2023-09-28" @default.
- W2023189967 title "Delayed Loss of Stability in Systems with Degenerate Linear Parts" @default.
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- W2023189967 doi "https://doi.org/10.4171/zaa/1154" @default.
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