Geodesic
Stable periodic solutions in scalar periodic differential delay equations
Archivum mathematicum, Tome 59 (2023) no. 1, pp. 69-76 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A class of nonlinear simple form differential delay equations with a $T$-periodic coefficient and a constant delay $\tau >0$ is considered. It is shown that for an arbitrary value of the period $T>4\tau -d_0$, for some $d_0>0$, there is an equation in the class such that it possesses an asymptotically stable $T$-period solution. The periodic solutions are constructed explicitly for the piecewise constant nonlinearities and the periodic coefficients involved, by reduction of the problem to one-dimensional maps. The periodic solutions and their stability properties are shown to persist when the nonlinearities are “smoothed” at the discontinuity points.
A class of nonlinear simple form differential delay equations with a $T$-periodic coefficient and a constant delay $\tau >0$ is considered. It is shown that for an arbitrary value of the period $T>4\tau -d_0$, for some $d_0>0$, there is an equation in the class such that it possesses an asymptotically stable $T$-period solution. The periodic solutions are constructed explicitly for the piecewise constant nonlinearities and the periodic coefficients involved, by reduction of the problem to one-dimensional maps. The periodic solutions and their stability properties are shown to persist when the nonlinearities are “smoothed” at the discontinuity points.
DOI : 10.5817/AM2023-1-69
Classification : 34K13, 34K20, 34K39
Keywords: delay differential equations; nonlinear negative feedback; periodic coefficients; periodic solutions; stability 
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Ivanov, Anatoli; Shelyag, Sergiy. Stable periodic solutions in scalar periodic differential delay equations. Archivum mathematicum, Tome 59 (2023) no. 1, pp. 69-76. doi: 10.5817/AM2023-1-69

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