# American Institute of Mathematical Sciences

November  2017, 22(9): 3483-3498. doi: 10.3934/dcdsb.2017176

## Dynamic behavior of a stochastic predator-prey system under regime switching

 1 Faculty of Mathematics, Mechanics, and Informatics, University of Science-VNU, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam 2 Department of Mathematics, Vinh University, 182 Le Duan, Vinh, Nghe An, Vietnam 3 Faculty of Basic Sciences, Ho Chi Minh University of Transport, 2 D3, Ho Chi Minh, Vietnam

* Corresponding author: Nguyen Thanh Dieu

Received  July 2016 Revised  May 2017 Published  July 2017

Fund Project: This work was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) n0 101.03-2017.23

In this paper we deal with regime switching predator-prey models perturbed by white noise. We give a threshold by which we know whenever a switching predator-prey system is eventually extinct or permanent. We also give some numerical solutions to illustrate that under the regime switching, the permanence or extinction of the switching system may be very different from the dynamics in each fixed state.

Citation: Nguyen Huu Du, Nguyen Thanh Dieu, Tran Dinh Tuong. Dynamic behavior of a stochastic predator-prey system under regime switching. Discrete & Continuous Dynamical Systems - B, 2017, 22 (9) : 3483-3498. doi: 10.3934/dcdsb.2017176
##### References:

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##### References:
Trajectories of $Y(t)$ in the state 1 (blue line) and in the state 2 (red line) in Ex. 1
A switching trajectory $Y(t)$ in Ex. 1.
Trajectories of $Y(t)$ in the first state (blue line) and the second state (red line) respectively in Ex. 2
A switching trajectory $Y(t)$ in Ex. 2
Phase picture and empirical density of $\big(X(t), Y(t)\big)$ in Ex. $3.2$ in 2D and 3D settings respectively
Values of the coefficients in Ex. 3.1
 $a_1$ $a_2$ $b_1$ $b_2$ $c_1$ $c_2$ $\sigma$ $\rho$ 1 0.9 2.5 2 2.8 0.6 5 0.6 4 2 0.2 0.1 1 4 3 0.5 1.5 4
 $a_1$ $a_2$ $b_1$ $b_2$ $c_1$ $c_2$ $\sigma$ $\rho$ 1 0.9 2.5 2 2.8 0.6 5 0.6 4 2 0.2 0.1 1 4 3 0.5 1.5 4
Values of the coefficients in Ex. 3.2
 $a_1$ $a_2$ $b_1$ $b_2$ $c_1$ $c_2$ $\sigma$ $\rho$ 1 0.2 0.45 1 9.5 5 1 2 4 2 1 0.85 0.5 3.6 4.2 2 1.5 4
 $a_1$ $a_2$ $b_1$ $b_2$ $c_1$ $c_2$ $\sigma$ $\rho$ 1 0.2 0.45 1 9.5 5 1 2 4 2 1 0.85 0.5 3.6 4.2 2 1.5 4
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