A periodic solution of period two of a delay differential equation

2018/01/28 by Nakata, Yukihiko
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.09244

Abstract

In this paper we prove that the following delay differential equation (d)/(dt)x(t)=rx(t)(1-∫₀¹x(t-s)ds), has a periodic solution of period two for r>\fracπ²2 (when the steady state, x=1, is unstable). In order to find the periodic solution, we study an integrable system of ordinary differential equations, following the idea by Kaplan and Yorke \citeKaplan=000026Yorke:1974. The periodic solution is expressed in terms of the Jacobi elliptic functions.

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