| Citation: |
Ningning Ye, Long Zhang, Zhidong Teng. THE DYNAMICAL BEHAVIOR AND PERIODIC SOLUTION IN DELAYED NONAUTONOMOUS CHEMOSTAT MODELS[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 156-183. doi: 10.11948/20210452
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THE DYNAMICAL BEHAVIOR AND PERIODIC SOLUTION IN DELAYED NONAUTONOMOUS CHEMOSTAT MODELS
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Abstract
In this paper, the global dynamics and existence of positive periodic solutions in a general delayed nonautonomous chemostat model are investigated. The positivity and ultimate boundedness of solutions are firstly obtained. The sufficient conditions on the uniform persistence and strong persistence of solutions are established. Furthermore, the criterion on the global attractivity of trivial solution is also established. As the applications of main results, the periodic delayed chemostat model is discussed, and the necessary and sufficient criteria on the existence of positive periodic solutions, and uniform persistence and extinction of microorganism species are obtained. Lastly, the numerical examples are presented to illustrate the main conclusions.
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References
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Ningning Ye, Long Zhang, Zhidong Teng. THE DYNAMICAL BEHAVIOR AND PERIODIC SOLUTION IN DELAYED NONAUTONOMOUS CHEMOSTAT MODELS[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 156-183. doi: 10.11948/20210452
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Figure 1.
(a): the numerical simulation of
$ s^*(t) $ $ (s(\eta), x(\eta))=(0.2+0.01i, 3.6+0.01i) $ $ \eta\in[-1.1, 0] $ $ i=1, 2, ... , 20 $ $ t\rightarrow \infty $ -
Figure 2.
(a): the numerical simulation of
$ s^*(t) $ $ (s(\eta), x(\eta))=(0.1+0.01i, 0.2+0.01i) $ $ \eta\in[-1, 0] $ $ i=1, 2, ... , 20 $ $ t\rightarrow \infty $ -
Figure 3.
(a): the numerical simulation of
$ s^*(t) $ $ (s(\eta), x(\eta))=(6.2+0.2i, 0.5+0.2i) $ $ \eta\in[-1.1, 0] $ $ i=1, 2, ... , 20 $ $ (s^*(t), 0) $ $ t\to\infty $ -
Figure 4.
(a): the numerical simulation of
$ s^*(t) $ $ (s(\eta), x(\eta))=(0.5+0.02i, 0.4+0.03i) $ $ \eta\in[-1, 0] $ $ i=1, 2, ... , 20 $ $ (s^*(t), 0) $ $ t\to\infty $