DYNAMIC COMPLEXITIES OF A CHEMOSTAT MODEL WITH PULSED INPUT AND WASHOUT AT DIFFERENT TIMES

Shuwen Zhang (), Dejun Tan and Hongsheng Gu
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Shuwen Zhang: College of Sciences, Jimei University, Xiamen, Fujian, 361021, P. R. China
Dejun Tan: College of Sciences, Jimei University, Xiamen, Fujian, 361021, P. R. China
Hongsheng Gu: Department of Mathematics, Anshan Normal University, Anshan, Liaoning, 114005, P. R. China

Advances in Complex Systems (ACS), 2008, vol. 11, issue 01, 65-76

Abstract: In this paper, we consider a predator–prey chemostat model with ratio-dependent Monod type functional response and periodic input and washout at different fixed times. We obtain an exact periodic solution with substrate and prey. The stability analysis for this periodic solutions yields an invasion threshold for the period of pulses of the predator. When the impulsive period is more than the threshold, there are periodic oscillations in the substrate, prey, and predator. If the impulsive period further increases, the system undergoes a complex dynamic process. By analyzing bifurcation diagrams, we can see that the impulsive system shows two kinds of bifurcation, which are period-doubling and period-halving.

Keywords: Predator–prey system; impulsive invasion and washout; chemostat; complexity (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1142/S0219525908001490

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