Global Stability of Wright-Type Equations with Negative Schwarzian

Abstract. Simplicity of the 37/24-global stability criterion announced by E. M. Wright in 1955 and rigorously proved by B. Bánhelyi et al. in 2014 for the delayed logistic equation raised the question of its possible extension for other population models. In our study, we answer this question by extending the 37/24-stability condition for the Wright-type equations with decreasing smooth nonlinearity [Formula: see text] which has a negative Schwarzian and satisfies the standard negative feedback and boundedness assumptions. The proof contains the construction and careful analysis of qualitative properties of certain bounding relations. To validate our conclusions, these relations are evaluated at finite sets of points; for this purpose, we systematically use interval analysis.