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

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. This is the second version: many typos have been corrected, the three figures have been amended, some statements have been clarified. We thank the anonimous referee for the help