On multistability of equations with a distributed delay, monotone production and the Allee effect

We consider the delay population dynamics model d N / d t = f ( N τ ( t ) ) − d ( N ( t ) ) with an increasing fecundity function f and any mortality function d where the Allee effect or multistability can be observed. The study includes non-autonomous equations with a distributed delay. Attractivity of certain positive solutions, persistence, extinction of solutions with initial values below a threshold, boundedness and oscillation are discussed.