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Study of a Monod-Haldene type food chain chemostat with pulsed substrate. (English) Zbl 1135.92035
Summary: We introduce and study a model of a Monod-Haldene type food chain chemostat with pulsed substrate. We investigate the 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 solutions 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, whose are period-doubling and period-halfing.

MSC:
92D40 Ecology
34C60 Qualitative investigation and simulation of ordinary differential equation models
34C25 Periodic solutions to ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C23 Bifurcation theory for ordinary differential equations
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