The problem of analyzing the mechanisms of variability in population dynamics caused by the combined influence of the Allee effect, immigration and random fluctuations is addressed. In this study, we explore such a multi-factorial problem based on a Ricker-type population model. For the deterministic version of the model, the transformations of system dynamic regimes caused by changes in parameters of growth rate and intensity of immigration are determined using bifurcation analysis. For the randomly forced population model, the phenomena of stochastic excitement and noise-induced temporal extinction are revealed and investigated. The parametric study of these effects uses statistical data obtained from direct numerical modeling as well as an analytical approach based on the stochastic sensitivity technique and the confidence interval method.
Ryashko et al. (Thu,) studied this question.