Existence and Uniqueness of Solutions to the Multispecies Virtual Population Analysis Equations

Abstract

This paper deals with the question of existence and uniqueness of solutions of multispecies virtual population analysis equations for predator–systems. By formulating the question as a fized-point problem for a certain function F, it is shown that at least one solution always exits. By using Brouwer degree, sufficient conditions for uniqueness are derived which are more likely to be satisfied than those based on the requirement that F be a contraction. Some of these are formulated as inequlities which could be verified in the course of solving the equations numerically.

virtual population analysis, predator-prey systems, fisheries models, fixed-point theorems, fixed-point index, Brouwer degree