Quasipolynomial generalization of Lotka-Volterra mappings

TL;DR

This paper extends the quasipolynomial formalism, previously used for differential equations, to discrete-time Lotka-Volterra mappings, providing a new framework for their analysis and applications in various scientific fields.

Contribution

It demonstrates the extension of quasipolynomial methods to discrete-time mappings, broadening the theoretical and practical understanding of Lotka-Volterra systems.

Findings

Quasipolynomial formalism is applicable to discrete-time Lotka-Volterra mappings.

The extension enables new algebraic methods for analyzing these mappings.

It opens new avenues for applications across different scientific disciplines.

Abstract

In the last years it has been shown that Lotka-Volterra mappings constitute a valuable tool from both the theoretical and the applied points of view, with developments in very diverse fields such as Physics, Population Dynamics, Chemistry and Economy. The purpose of this work is to demonstrate that many of the most important ideas and algebraic methods that constitute the basis of the quasipolynomial formalism (originally conceived for the analysis of ordinary differential equations) can be extended into the mapping domain. The extension of the formalism into the discrete-time context is remarkable as far as the quasipolynomial methodology had never been shown to be applicable beyond the differential case. It will be demonstrated that Lotka-Volterra mappings play a central role in the quasipolynomial formalism for the discrete-time case. Moreover, the extension of the formalism into the discrete-time domain allows a significant generalization of Lotka-Volterra mappings as well as a whole transfer of algebraic methods into the discrete-time context. The result is a novel and more general conceptual framework for the understanding of Lotka-Volterra mappings, as well as a new range of possibilities that becomes open not only for the theoretical analysis of Lotka-Volterra mappings and their generalizations, but also for the development of new applications.