Abstract
In this paper we consider a chemostat-like model for a simple food chain of microorganisms. This consists of a well stirred nutrient substance that is the food for a prey population of microorganism. At the bottom of the food chain there is a predator population of miroorganisms that grows up on the prey. The nutrient-uptake of each population is of Holling type I (or Lotka-Volterra) form. We show the existence of the global attractor for the solutions of the model and also we show that the positive globally asymptotically stable equilibrium point of the system undergoes a Hopf bifurcation when we suppose that the dynamic of the microorganisms at the bottom of the chain depend on the past history of the prey population by mean a distributed delay that take an average of the microorganisms in the middle of the chain.
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Cavani, M., Romero, S. A Simple Food Chain Model with Delay. In: Benvenuti, L., De Santis, A., Farina, L. (eds) Positive Systems. Lecture Notes in Control and Information Science, vol 294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44928-7_37
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DOI: https://doi.org/10.1007/978-3-540-44928-7_37
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40342-5
Online ISBN: 978-3-540-44928-7
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