Impact of time delay on population model with Allee effect

•A general delayed population system with Allee effect is investigated•The influence of strong and weak Allee effect on population system are different•Strong Allee effect is beneficial to the stability and survival of population•The phenomenon of resonant activation is discovered in biology with Allee effect We investigate a general delayed stochastic single-species population system with Allee effect simulated by coupling between non-Gaussian colored noise and Gaussian white noise. Firstly, the Fokker–Planck function is derived through unified colored noise approximation (UCNA) and small time delay approximation. Then, the expression of stationary probability distribution is obtained. After that, the expression of mean first-passage time is calculated in order to quantify the transition between stable states. Besides, The influence of strong Allee effect and weak Allee effect on the stochastic population system is different. It is not conducive to the survival of the population when the intensity of multiplicative non-Gaussian colored noise is enhanced whether strong Allee effect or weak Allee effect exists. It is beneficial to the stability and survival for the population under strong Allee effect. Further, the phenomenon of resonant activation is firstly discovered in biological system with Allee effect. The increase of time delay will restrain the transition between stable states under strong Allee effect. When weak Allee effect exists, the increase of time delay will reduce stability of the population, even the population may be vulnerable to extinction. The results in our work provide effective guidance for future researches of ecosystem.