Regular and chaotic variability caused by random disturbances in a predator–prey system with disease in predator

Abstract

A “prey–predator” population model when the predator population is susceptible to disease is considered. We perform a deterministic bifurcation analysis in dependence on the infection rate parameter and specify multistability zones with coexistence of equilibrium and oscillatory modes. In this model, we study stochastic effects caused by random fluctuations in the predation rate and infection rate parameters. Noise-induced transitions between equilibrium and oscillatory modes are studied both numerically and analytically by the stochastic sensitivity approach. An opposite of consequences of random perturbations in two different parameters, namely noise-induced regularization or transition to chaos, is discovered and justified by Lyapunov exponents.