GLOBAL DYNAMICS ANALYSIS OF A NONLINEAR IMPULSIVE STOCHASTIC CHEMOSTAT SYSTEM IN A POLLUTED ENVIRONMENT

Xinzhu Meng; Lu Wang; Tonghua Zhang

doi:10.11948/2016055

2016 Volume 6 Issue 3

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Xinzhu Meng, Lu Wang, Tonghua Zhang. GLOBAL DYNAMICS ANALYSIS OF A NONLINEAR IMPULSIVE STOCHASTIC CHEMOSTAT SYSTEM IN A POLLUTED ENVIRONMENT[J]. Journal of Applied Analysis & Computation, 2016, 6(3): 865-875. doi: 10.11948/2016055

Citation:

Xinzhu Meng, Lu Wang, Tonghua Zhang. GLOBAL DYNAMICS ANALYSIS OF A NONLINEAR IMPULSIVE STOCHASTIC CHEMOSTAT SYSTEM IN A POLLUTED ENVIRONMENT[J]. Journal of Applied Analysis & Computation, 2016, 6(3): 865-875. doi: 10.11948/2016055

GLOBAL DYNAMICS ANALYSIS OF A NONLINEAR IMPULSIVE STOCHASTIC CHEMOSTAT SYSTEM IN A POLLUTED ENVIRONMENT

1 State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, P. R. China;
2 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China;
3 Department of Mathematics, Swinburne University of Technology, Hawthorn, VIC 3122, Australia

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Abstract

Abstract

This paper intends to develop a new method to obtain the threshold of an impulsive stochastic chemostat model with saturated growth rate in a polluted environment. By using the theory of impulsive differential equations and stochastic differential equations, we obtain conditions for the extinction and the permanence of the microorganisms of the deterministic chemostat model and the stochastic chemostat model. We develop a new numerical computation method for impulsive stochastic differential system to simulate and illustrate our theoretical conclusions. The biological results show that a small stochastic disturbance can cause the microorganism to die out, that is, a permanent deterministic system can go to extinction under the white noise stochastic disturbance. The theoretical method can also be used to explore the threshold of some impulsive stochastic differential equations.
- Stochastic chemostat model /
- impulsive stochastic differential equations /
- extinction /
- permanence in mean /
- saturated growth rate
MSC: 34D23;34K20;92D30

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