# American Institute of Mathematical Sciences

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September  2017, 22(7): 2651-2667. doi: 10.3934/dcdsb.2017129

## Extinction in stochastic predator-prey population model with Allee effect on prey

 University of Niš, Faculty of Sciences and Mathematics, Višegradska 33,18000 Niš, Serbia

* Corresponding author: Miljana Jovanović

Received  July 2016 Revised  December 2016 Published  April 2017

Fund Project: The authors were supported by the Grant No 174007 of MNTRS.

This paper presents the analysis of the conditions which lead the stochastic predator-prey model with Allee effect on prey population to extinction. In order to find these conditions we first prove the existence and uniqueness of global positive solution of considered model using the comparison theorem for stochastic differential equations. Then, we establish the conditions under which extinction of predator and prey populations occur. We also find the conditions for parameters of the model under which the solution of the system is globally attractive in mean. Finally, the numerical illustration with real life example is carried out to confirm our theoretical results.

Citation: Miljana JovanoviĆ, Marija KrstiĆ. Extinction in stochastic predator-prey population model with Allee effect on prey. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2651-2667. doi: 10.3934/dcdsb.2017129
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##### References:
Deterministic and stochastic trajectories of moose and wolf population described by (2) with parameters (12), $\alpha=0.0002$, $A_1=0.5$, $\sigma_1^2=\sigma_2^2=0.005$
Left: Deterministic and stochastic trajectories of moose population described by (2) with parameters (12), $\alpha=0.0002$, $A_1=5$, $\sigma_1^2=\sigma_2^2=0.005$; Right: Stochastic trajectories of moose and wolf populations in which we can observe behavior of these populations in 140 years
Deterministic and stochastic trajectories of moose population described by (2) with parameters (12), $\alpha=0.01$, $A_1=0.5$ and different intensities of noise
Deterministic and stochastic trajectories of moose and wolf population described by (2) with parameters (12), $\alpha=0.01$, $A_1=5$, $\sigma_1^2=0.14$, $\sigma_2^2=0.005$
Stochastic trajectories of moose and wolf population described by (2) with three different initial values
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