The author of this interesting paper investigates the partial functional differential equation \[ \partial u(x,t)\partial t =k \partial^2 u(x,t)\partial x^2+ru(x,t-T)[1-u(x,t)], \;\;t\geq 0, \;\;x\in [{}0,\pi ]{} \] under the boundary condition \(u(0,t)=u(\pi ,t)=0\) (\(t>0\)) and \(u(x,s)=\phi (x,s)\), \(-T\leq s\leq 0\), \(0\leq x\leq \pi \). This problem describes a model for population density with a time delay and self-regulation. An interesting task here is to explain oscillations in numerical simulations as being a Hopf bifurcation phenomenon. In particular it was investigated by W.C. Chan and D. Green (1993). In this paper, the author proves that a much simpler behavior should have been observed, namely the convergence to a nontrivial time-independent equilibrium. Also it is established the stability of \(u=0\) for \(rk\) is shown. Numerical simulations illustrate the main results. Exponential decay for \(r