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Bifurcation and chaos in a Monod-Haldane type food chain chemostat with pulsed input and washout. (English) Zbl 1130.92058
Summary: We introduce and study a model of a Monod-Haldane type food chain chemostat with pulsed input and washout. We investigate a subsystem with substrate and prey and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, prey and predator. Simple cycles may give way to chaos in a cascade of period-doubling bifurcations. Furthermore, by comparing bifurcation diagrams with different bifurcation parameters, we can see that the impulsive system shows two kinds of bifurcations, which are period-doubling and period-halving.

92D40 Ecology
34C60 Qualitative investigation and simulation of ordinary differential equation models
34A37 Ordinary differential equations with impulses
34C28 Complex behavior and chaotic systems of ordinary differential equations
37N25 Dynamical systems in biology
Full Text: DOI
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