Modeling Dynamics of Complex System with Solutions of the Generalized Lotka-Volterra Equations

Abstract

A system of nonlinear ordinary differential equations with forcing function is developed to model evolution processes in complex systems. In this system R, C, and P are the resource, consumption, and production functions correspondingly. F is the forcing function. Two cases F=0, and F=A+Bsin(omega x t) are considered. It is shown that if F=0, there exist an unstable periodic solution for a certain set of system coefficients. In the case of periodic forcing, system has an attractor solution. The system developed may have a wide range of applications: in biological and social sciences, in economics, in ecology, and, as well, in modeling climate. A correspondence between the theoretical (numerical) solution and Late Pleistocene climate data dynamics is analyzed on a qualitative level.