| Citation: |
Miaomiao Gao, Daqing Jiang, Tasawar Hayat, Ahmed Alsaedi, Bashir Ahmad. DYNAMICS OF A STOCHASTIC CHEMOSTAT COMPETITION MODEL WITH PLASMID-BEARING AND PLASMID-FREE ORGANISMS[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1464-1481. doi: 10.11948/20190236
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DYNAMICS OF A STOCHASTIC CHEMOSTAT COMPETITION MODEL WITH PLASMID-BEARING AND PLASMID-FREE ORGANISMS
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Abstract
In this paper, we consider a chemostat model of competition between plasmid-bearing and plasmid-free organisms, perturbed by white noise. Firstly, we prove the existence and uniqueness of the global positive solution. Then by constructing suitable Lyapunov functions, we establish sufficient conditions for the existence of a unique ergodic stationary distribution. Furthermore, conditions for extinction of plasmid-bearing organisms are obtained. Theoretical analysis indicates that large noise intensity $\sigma_{2}^{2}$ is detrimental to the survival of plasmid-bearing organisms and is not conducive to the commercial production of genetically altered organisms. Finally, numerical simulations are presented to illustrate the results. -
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References
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Miaomiao Gao, Daqing Jiang, Tasawar Hayat, Ahmed Alsaedi, Bashir Ahmad. DYNAMICS OF A STOCHASTIC CHEMOSTAT COMPETITION MODEL WITH PLASMID-BEARING AND PLASMID-FREE ORGANISMS[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1464-1481. doi: 10.11948/20190236
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Figure 1. The pictures on the left are the solutions of system (2.1). The pictures on the right are the density functions of system (2.1) with initial value
$ (s(0),x(0),y(0)) = (1,1,0.04) $ ,$ \sigma_{1}^2 = 0.0225,\;\sigma_{2}^2 = 0.01,\;\sigma_{3}^2 = 0.01 $ ,$ q = 0.005 $ . (Color figure online) -
Figure 2. The solutions of system (2.1) with initial value
$ (s(0),x(0),y(0)) = (1,1,0.04) $ ,$ \sigma_{1}^2 = 0.0225,\;\sigma_{2}^2 = 0.9025,\;\sigma_{3}^2 = 0.01 $ ,$ q = 0.5 $ . (Color figure online)