Qualitative analysis of generalized volterra models

Generalized Volterra models are analyzed qualitatively to provide some information concerning their applicability as ecological-model estimators. For the general two-population system (including prey-predator, competitive, and other cases), the stability of the equilibrium points and other properties of the phase representation are investigated. For n-population systems, stability analysis is carried out mainly by means of several Liapunov functions. The persistence (or global stability of nontrivial equilibrium) of n-population systems is investigated, leading to an interaction-exclusion principle which implies restrictions on the interaction structure of the system, especially in the case of trophic systems.