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Analysis of Stochastic Bifurcations in the Eco-Epidemiological Oscillatory Model with Weak Allee Effect

An eco-epidemiological model of dynamical interaction of susceptible prey, infected prey, and predator is studied in the presence of the Allee effect and random disturbances. A bifurcation analysis of the deterministic variant of the model versus Allee parameter is carried out. Various regimes of tri-rhythmicity with coexistence of three cycles, or two cycles and one chaotic attractor are revealed. The complication of population dynamics due to stochastic transitions between coexisting oscillatory attractors and order-chaos transformations is studied both numerically and analytically, by the method of confidence ellipsoids and tori. The phenomenon of noise-induced extinction of predator with increasing amplitudes of oscillations for susceptible or infected prey is discussed.