Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 76, pp. 1-10.

Title: Hopf bifurcation for simple food chain model with delay

Authors: Mario Cavani (Univ. de Oriente, Cumana, Venezuela)
         Teodoro Lara (Univ. Rafael Rangel, Trujillo, Venezuela)
	 Sael Romero  (Univ. de Oriente, Cumana, Venezuela)

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.