Analysis of the influence of parametric noise on the dynamics of two interacting populations

This paper considers the predator-prey population model, which combines both the stabilizing factors of the intraspecific competition of prey and predator (for resources other than the prey), and the predator saturation. The purpose of this study is a comparative parametric analysis of stochastic phenomena which occur under parametric noise of two different types. The stochastic sensitivity of the attractors is studied. Based on the stochastic sensitivity function technique, noise-induced phenomena are described. In the parametric bistable zone, transitions of two types are carried out: equilibrium → equilibrium and cycle → equilibrium. The values of critical intensities for the occurrence of transition phenomena between attractors are obtained. In the parametric monostable zone, such phenomena as cycle deformation and equilibrium shift are demonstrated. © 2019 Udmurt State University. All right reserved. Russian Science Foundation, RSF: 16–11–10098 Funding. The research was supported by the Russian Science Foundation (project no. 16–11–10098).