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

  • * Corresponding author: Nguyen Thanh Dieu

    * Corresponding author: Nguyen Thanh Dieu 

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

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  • 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.

    Mathematics Subject Classification: 37A25, 60J60, 92D25.

    Citation:

    \begin{equation} \\ \end{equation}
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  • Figure 1.  Trajectories of $Y(t)$ in the state 1 (blue line) and in the state 2 (red line) in Ex. 1

    Figure 2.  A switching trajectory $Y(t)$ in Ex. 1.

    Figure 3.  Trajectories of $Y(t)$ in the first state (blue line) and the second state (red line) respectively in Ex. 2

    Figure 4.  A switching trajectory $Y(t)$ in Ex. 2

    Figure 5.  Phase picture and empirical density of $\big(X(t), Y(t)\big)$ in Ex. $3.2$ in 2D and 3D settings respectively

    Table 1.  Values of the coefficients in Ex. 3.1

    $a_1$ $a_2$ $b_1$ $b_2$ $c_1$ $c_2$ $\sigma$ $\rho$
    10.92.522.80.650.64
    20.20.11430.51.54
     | Show Table
    DownLoad: CSV

    Table 2.  Values of the coefficients in Ex. 3.2

    $a_1$ $a_2$ $b_1$ $b_2$ $c_1$ $c_2$ $\sigma$ $\rho$
    10.20.4519.55124
    210.850.53.64.221.54
     | Show Table
    DownLoad: CSV
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