The Volterra Integrable case. Novel analytical and numerical results

TL;DR

This paper revisits the integrable Hamiltonian N-species Volterra system, introducing new analytical and numerical methods, conserved quantities, and solutions, extending classical predator-prey models to more complex multi-species interactions.

Contribution

It presents a novel approach to constructing conserved quantities and provides new analytical and numerical results for the integrable Volterra system, expanding previous work.

Findings

New conserved quantities for the N-species Volterra system

Analytical solutions for classical predator-prey models

Numerical simulations confirming integrability and solution behavior

Abstract

In the present paper we reconsider the integrable case of the Hamiltonian $N$-species Volterra system, as it has been introduced by Vito Volterra in 1937 and significantly enrich the results already published in the ArXiv in 2019 by two of the present authors (M. Scalia and O. Ragnisco). In fact, we present a new approach to the construction of conserved quantities and comment about the solutions of the equations of motion; we display mostly new analytical and numerical results, starting from the classical predator-prey model and arriving at the general $N$-species model