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

Articles in Press

Document Type : Research Article

Authors

• Debjani Mondal
• Moitri Sen
• Partha Sarathi Mandal

Department of Mathematics, National Institute of Technology Patna, Patna, Bihar, India.

10.22067/ijnao.2024.88668.1463

Abstract

In this study, Allee type, single-species (prey), two-patch model with non-linear harvesting rate and species migration across two patches have been developed and analysed. As we all know, the population of any species in an ecosystem is greatly dependent on the carrying capacity of the corresponding ecosystem; the main focus of our work is on how carrying capacity affects system dynamics in the presence and absence of randomness (deterministic and stochastic case, respectively). In deterministic case, we find that the carrying capacity of both patches increases the number of interior equilibrium points, and a maximum of eight interior equilibrium 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 (CTMC) modelling approach to construct an equivalent stochastic model of the corresponding deterministic 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 stochasticity 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.

Keywords

• Stability analysis
• Bifurcation
• Continuous time Markov chain (CTMC)
• Expected time to extinction

Main Subjects

• Modeling and Simulation

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