Abstract

The study of many aspects of the qualitative theory of difference equations and delay differential equations was classically motivated by the analysis of population models.
In some famous equations with a unique positive equilibrium K, one of the unsolved problems is whether the local asymptotic stability of K implies its global stability. It is our purpose to show a new approach, which allows us to relate and support three of the most celebrated conjectures in this subject: the Wright conjecture (1955) for the delayed continuous logistic equation, the Levin and May conjecture (1976) for the delayed discrete logistic equation, and the Smith conjecture (1995) for the Nicholson′s blowflies equation.