Global stability for a class of functional differential equations with distributed delay and non-monotone bistable nonlinearity

Abstract

The present work is devoted to the global stability analysis for a class of functional differential equations with distributed delay and non-monotone bistable nonlinearity. First, we characterize some subsets of attraction basins of equilibria. Next, by Lyapunov functional and fluctuation method, we obtain a series of criteria for the global stability of equilibria. Finally, we illustrate our results by applying them to a problem with Allee effect.

Keywords

• distributed delay
• bistable nonlinearity
• global stability
• lyapunov functional
• allee effect