Mario Cavani, Teodoro Lara, Sael Romero
Abstract:
In this article we consider a chemostat-like model for a
simple food chain where there is a well stirred nutrient substance
that serves as food for a prey population of microorganisms,
which in turn, is the food for a predator population of microorganisms.
The nutrient-uptake of each microorganism is of Holling type I
(or Lotka-Volterra) form.
We show the existence of a global attractor for solutions of this
system. Also we show that the positive globally asymptotically stable
equilibrium point of the system undergoes a Hopf bifurcation when
the dynamics of the microorganisms at the bottom of the chain depends
on the history of the prey population by means of a distributed
delay that takes an average of the microorganism in the middle of
the chain.
Submitted May 11, 2009. Published June 16, 2009.
Math Subject Classifications: 34D99
Key Words: Simple food chain model; Hopf bifurcation;
Holling type I; attractor.
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Mario Cavani Departamento de Matemáticas, Núcleo de Sucre Universidad de Oriente, Cumaná 6101, Venezuela email: mcavani@sucre.udo.edu.ve |
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Teodoro Lara Departamento de Física y Matemáticas, Universidad de los Andes Núcleo Univeristario Rafael Rangel, Trujillo, Venezuela email: tlara@ula.ve |
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Sael Romero Departamento de Matemáticas, Núcleo de Sucre Universidad de Oriente, Cumaná 6101, Venezuela email: sromero@sucre.udo.edu.ve |
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