A Homotopy Technique for a Linear Generalization of Volterra Models

Abstract

The classical Lotka-Volterra models from papulation dynamics have the structure of the system of O.D.E.

$$\frac{{d{x_i}}}{{dt}} = {x_i}({e_i} + \sum\limits_{j \in N} {{a_{ij}}{x_j}} ){\text{ }},{\text{ }}i \in N{\text{ }},$$

Math where N = }1,2,…,n} is the set of all the indices of the variables, e_i, a_ij, i,j ∈ N are suitable real parameters and x_i = x_i(t) represents the density or the biomass of i-th species at time t.