Stochastic Canards in a Modified Leslie–Gower Population Model

The problem of analyzing the bifurcation mechanisms of complex stochastic oscillations in population dynamics is considered. We study this problem on the basis of the modified Leslie–Gower prey–predator model with randomly forced Holling-II functional response. The paper focuses on the effects of noise in the Canard explosion zone. The phenomenon of noise-induced splitting of Canard cycles is discovered and studied in terms of stochastic P-bifurcations. In parametric analysis, we use the stochastic sensitivity technique with the apparatus of confidence domains to find the most noise-sensitive Canard. For the phenomenon of stochastic splitting, an underlying deterministic mechanism using critical curves near the cycle orbit and sub-/super-critical zones is revealed.