Persistence and Stability of a Food Chain Model with Mixed Selection of Functional Responses - Maiti, A.; Patra, B.; Samanta, G. P. (Nonlinear Analysis: Modelling and Control, 2006)
One approach to the study of an ecological community begins with an important object: its food web. Theoretical studies of food web must contend with the question of how to couple the large number of interacting species. One line of investigation assumes that the “building blocks” are species interacting in a pairwise fashion. The model we analyze in this paper describes a tritrophic food chain composed of logistic prey, a classical Lotka-Volterra functional response for prey and predator, and a Holling type-II functional response for predator and superpredator. Dynamical behaviours such as boundedness, stability, persistence, bifurcation et cetera of the model are studied critically. Computer simulations are carried out to explain the analytical findings. Finally it is discussed how these ideas illuminate some of the observed properties of real populations in the field, and explores practical implications.
Keywords: food chain model; boundedness; persistence; stability; Hopf bifurcation