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

Abstract

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.

Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger

“…Moreover, for discrete-time systems, the theory of stochastic sensitivity was elaborated also for closed invariant curves [35] and chaotic attractors [36]. This theory is effectively used in the stochastic analysis of nonlinear dynamic models in various fields of science (see, e.g., [33,[37][38][39]), and also in control problems [40,41]. Geometrically, the stochastic sensitivity function technique can be applied in the form of confidence domains [29,32].…”

“…However, direct use of this equation encounters serious mathematical difficulties even in two-dimensional cases, so asymptotics and approximations are helpful [25,26]. Among others, the stochastic sensitivity function technique is a useful constructive tool for studying phenomena caused by noise (see, e.g., [27][28][29][30][31][32][33]).…”