Growth Phenomena — Algebraic and Geometric Descriptions

Abstract

An enormous variety of nonlinear dynamical systems can be — by suitable introduction of new coordinates — represented in the form of polynomial systems and then can be reduced to Volterra systems, where the nonlinearities are at most quadratic. In this paper, we discuss a link between systems of differential equations with homogeneous quadratic polynomial vector fields and non-associative algebras on the one hand and the question of representation of such systems as geodesics in some Finsler spaces on the other hand.