Nicholson’s blowflies differential equations with a small delay in the mortality term

Abstract

For the Nicholson’s blowflies equation with delayed mortality N′(t)=m(t)−δN(h1(t))+PN(h2(t))e−γN(h2(t)),P>δ,positivity, persistence, and boundedness of solutions are established. Two global stability tests for the positive equilibrium are obtained based on a linearized global stability method, reducing stability of a non-linear model to a specially constructed linear equation. The first one extends the absolute stability result to the case of delayed mortality and the second test is delay-dependent.