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

Nguyen Huu Du; Nguyen Thanh Dieu; Tran Dinh Tuong

doi:10.3934/dcdsb.2017176

Article Contents

2017, Volume 22, Issue 9: 3483-3498. Doi: 10.3934/dcdsb.2017176

This issue Previous Article Numerical simulation of universal finite time behavior for parabolic IVP via geometric renormalization group Next Article On stochastic multi-group Lotka-Volterra ecosystems with regime switching

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
* Corresponding author: Nguyen Thanh Dieu

Received: July 2016

Revised: May 2017

Published: October 2017

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

Abstract / Introduction Full Text(HTML) Figure(5) / Table(2) Related Papers Cited by

Abstract

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.

Keywords:

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

Citation:

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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

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

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

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

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

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Table 1. 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

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Table 2. 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

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