Effects of predation efficiencies on the dynamics of a tritrophic food chain.

In this paper the dynamics of a tritrophic food chain (resource, consumer, top predator) is investigated, with particular attention not only to equilibrium states but also to cyclic behaviours that the system may exhibit. The analysis is performed in terms of two bifurcation parameters, denoted by p and q, which measure the efficiencies of the interaction processes. The persistence of the system is discussed, characterizing in the (p; q) plane the regions of existence and stability of biologically significant steady states and those of existence of limit cycles.

Modelling of predator-prey trophic interactions. Part II: three trophic levels.

A general class of lumped parameter models describing the local dynamics of a tri-trophic chain in a controlled environment is analyzed in detail. The trophic functions characterizing the interactions are defined only by some properties and allow us to treat both prey-dependent and ratio-dependent models in a unified manner. Conditions for existence and stability of extinction and coexistence equilibrium states are determined.