The integrable Volterra system in the case of infinitely many species, either countable or uncountable

TL;DR

This paper extends the integrability and superintegrability properties of the Volterra model to infinitely many species, providing analytical and numerical evidence for these properties in both countable and uncountable cases.

Contribution

It demonstrates that the superintegrability of the Volterra system applies to infinitely many species, expanding previous finite-species results.

Findings

Superintegrability extends to countably infinite species

Superintegrability extends to uncountably infinite species

Analytical and numerical validation of superintegrability

Abstract

In the present paper we derive a further extension of the results contained in two recent articles, both published in Open Communications in Nonlinear Mathematical Physics, where it was shown that the integrable version of the N-species Volterra model, introduced by V. Volterra in 1937, is in fact maximally superintegrable. Here we point out that the superintegrability property applies as well to the case of infinitely many competing species, either countable or uncountable. Analytical and numerical results are given.