Analysis of periodic solutions of a continuous dynamical system with delay and pumping (Q731612)

The authors study the periodic solutions of a continuous dynamical system with delay and pumping. Pumping is defined as the instant changes in phase coordinates in the system under certain conditions. The authors study the equation \[ x'(t)=-k x(t-1) \] with \(0 \leq t < \infty\) and \(x(t)=0 \Longrightarrow x(t^{+})=1\). The authors find all one-piece periodic solutions of the dynamical system. The suggested method involves the Euler Laplace integral transform.