Address:
Department of Mathematics, Pennsylvania State University, 44 University Drive, Dallas, PA 18612, USA
School of Information Technology, Deakin University, Melbourne, Victoria, 3125, Australia
E-mail:
afi1@psu.edu
sergiy.shelyag@deakin.edu.au
Abstract: 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.
AMSclassification: primary 34K13; secondary 34K20, 34K39.
Keywords: delay differential equations, nonlinear negative feedback, periodic coefficients, periodic solutions, stability.
DOI: 10.5817/AM2023-1-69