Dynamical behavior of a stochastic food chain chemostat model with Monod response functions |
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| Authors: | Miaomao Gao Daqing Jiang Kai Qi Tasawar Hayat Ahmed Alsaedi and Bashir Ahmad |
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| Institution: | College of Science, China University of Petroleum (East China), Qingdao 266580, China,College of Science, China University of Petroleum (East China), Qingdao 266580, China,College of Science, China University of Petroleum (East China), Qingdao 266580, China,Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia,Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia and Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia |
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| Abstract: | This paper studies a food chain chemostat model with Monod response functions, which is perturbed by white noise. Firstly, we prove the existence and uniqueness of the global positive solution. Then sufficient conditions for the existence of a unique ergodic stationary distribution are established by constructing suitable Lyapunov functions. Moreover, we consider the extinction of microbes in two cases. In the first case, both the predator and prey species are extinct. In the second case, only the predator species is extinct, and the prey species survives. Finally, numerical simulations are carried out to illustrate the theoretical results. |
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| Keywords: | Stochastic food chain chemostat model Monod response function stationary distribution extinction |
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