Complex dynamics of a chemostat with variable yield and periodically impulsive perturbation on the substrate |
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Authors: | Shulin Sun Lansun Chen |
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Institution: | (1) School of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen, 041004, Peoples Republic of china;(2) Department of Applied Mathematics, Dalian University of Technology, Liaoning, Dalian, 116024, Peoples Republic of china |
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Abstract: | In this paper, we consider the dynamic behaviors of a mathematical chemostat model with variable yield and periodically impulsive
perturbation on the substrate. The microbial growth rate is the Monod function and the variable yield coefficient δ(S) is quadratic (1 + cS
2). Using Floquet theory and small amplitude perturbation method, we establish the condition under which the boundary periodic
solution is globally asymptotically stable. Moreover, the permanence of the system is discussed in detail. Finally, by means
of numerical simulation, we demonstrate that with the increasing of the pulsed substrate in the feed the system exhibits the
complex dynamics.
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Keywords: | variable yield periodically pulsed substrate permanence chaotic attractor |
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