Geodesic
Hopf bifurcation for simple food chain model with delay
Electronic Journal of Differential Equations, Tome 2009 (2009).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 34D99
Keywords: simple food chain model, Hopf bifurcation, Holling type I, attractor 
@article{EJDE_2009__2009__a59,
     author = {Cavani, Mario and Lara, Teodoro and Romero, Sael},
     title = {Hopf bifurcation for simple food chain model with delay},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2009},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a59/}
}
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Cavani, Mario; Lara, Teodoro; Romero, Sael. Hopf bifurcation for simple food chain model with delay. Electronic Journal of Differential Equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a59/