On some realistic constraints in prey-predator mathematics

An augmented model in which conic section formulae appear as factors in the x 1 isocline expressions is suggested, as a way of overcoming this possibly ubiquitous defect of the classical system.

Abstract

Various analytical formulations are presented as candidates for ordinary differential equation models of competitive/predatory animal ecosystems. The two-species case is treated exhaustively, subject to certain realistic constraints. When these constraints were applied to computer simulations of a classical model with six and ten species, no non-trivial equilibrium points or limit cycles were found. As a way of overcoming this possibly ubiquitous defect of the classical system, an augmented model in which conic section formulae appear as factors in the ẋ1 isocline expressions is suggested.