Periodic solutions and hydra effect for delay differential equations with nonincreasing feedback
The authors consider a delay differential equation of the form \[ y'(t)=-\mu y(t)+f(y(t-1)) \] with \(\mu>0\) and a nonincreasing function \(f:\mathbb{R}\to(0,\infty)\). This equation models the change in time of the quantity \(y(t)\geq 0\) such that \(y\) decays with a rate proportional to \(y(t)\), and is produced with a rate \(f(y(t-1))\). The aim of this paper is to show analytically that hydra effect appears in the above equation. This phenomenon was observed recently in different mathematical models in population dynamics and is described by the fact that the size of the population can be increased by increasing the mortality rate.
scientific article; zbMATH DE number 6841281