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Keywords:
delay differential equations; nonlinear negative feedback; periodic coefficients; periodic solutions; stability
delay differential equations; nonlinear negative feedback; periodic coefficients; periodic solutions; stability
Summary:
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.
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