Effect of demographic stochasticity in the persistence zone of a two-patch model with nonlinear harvesting

In this study, Allee type, single-species (prey), two-patch model with nonlinear harvesting rate, and species migration across two patches have been developed and analyzed. As we all know, the population of any species in an ecosystem is greatly dependent on the carrying capacity of the corre-sponding ecosystem; the main focus of our work is on how carrying capacity affects system dynamics in the presence and absence of randomness (de-terministic and stochastic case, respectively). In the deterministic case, we find that the carrying capacity of both patches increases the number of interior equilibrium points, and a maximum of eight interior equilib-rium points can be observed. Also, we observe some interesting dynamics, including bi-stability, tri-stability, and catastrophic bifurcations. On the other hand, we use the continuous-time Markov chain modeling approach to construct an equivalent stochastic model of the corresponding determin-istic model based on deterministic assumptions. Based on the extinction or persistence of the species, we compare the dynamics of deterministic and stochastic models in order to assess the impact of demographic stochas-ticity on the population of the species in two patches. The stochastic model shows the possibility of species extinction in a finite amount of time, whereas the deterministic model shows the persistence of the species at the same time, which is the major difference between these two models. We also derive the implicit equation for the expected time needed for species extinction. Finally, a graphic is used to illustrate how the patch’s carrying capacity affects the expected time.