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The main aim of this paper is to establish sharp global stability conditions for the positive equilibrium of a well-known model of economic growth when a delay is considered in the production function. In order to deal with a broad scenario, we establish some results of global attraction for a general family of differential equations with variable delay; for it, we use the notion of strong attractor, which allows us to simplify the proofs, as well as to generalize previous results. Our study reveals that sometimes production delays are not able to destabilize the positive equilibrium, even if they are large. In other cases, the stability properties of the equilibrium depend on the interaction between the delay and other relevant model parameters, leading sometimes to stability windows in the bifurcation diagram.

We find the exact region of global stability for the $2$-periodic Ricker difference equation, showing that a $2$-periodic solution is globally asymptotically stable whenever it is locally asymptotically stable and the equation does not have more $2$-periodic solutions. We conjecture that this property holds for the general $p$-periodic Ricker difference equation, and in particular we prove it for $p=3$.