Geodesic
Hopf bifurcation for simple food chain model with delay
Electronic journal of differential equations, Tome 2009 (2009)
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},
     year = {2009},
     volume = {2009},
     zbl = {1176.34099},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a59/}
}
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AU  - Cavani,  Mario
AU  - Lara,  Teodoro
AU  - Romero,  Sael
TI  - Hopf bifurcation for simple food chain model with delay
JO  - Electronic journal of differential equations
PY  - 2009
VL  - 2009
UR  - http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a59/
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%0 Journal Article
%A Cavani,  Mario
%A Lara,  Teodoro
%A Romero,  Sael
%T Hopf bifurcation for simple food chain model with delay
%J Electronic journal of differential equations
%D 2009
%V 2009
%U http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a59/
%G en
%F EJDE_2009__2009__a59
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/