THE DYNAMICS OF A THREE-SPECIES FOOD CHAIN INTERACTION MODEL WITH MICHAELIS-MENTEN TYPE FUNCTIONAL RESPONSE
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Date
2011
Journal Title
Journal ISSN
Volume Title
Publisher
Journal of Sustainability Science and Management
Abstract
In this paper, we study an ecological model with a tritrophic food chain composed of
a classical Lotka-Volterra functional response for prey and predator, and a Michaelis-Mententype functional response for predator and top predator. There are two equilibrium points of the
system. In the parameter space, there are passages from instability to stability, which are called Hopf
bifurcation points. For the first equilibrium point, it is possible to find bifurcation points analytically
and to prove that the system has periodic solutions around these points. Furthermore the dynamical
behaviours of this model are investigated. The dynamical behaviour is found to be very sensitive to
parameter values as well as the parameters of the practical life. Computer simulations are carried
out to explain the analytical findings.
Description
Keywords
food-chain model, Hopf bifurcation, modified Latka-Volterra model, modified Michaelis-Menten-type functional response