Integrability of a class of N-dimensional Lotka-Volterra and Kolmogorov systems

We study the integrability of an N-dimensional differential Kolmogorov systems of the form (x) over dot(j) = x(j) (a(j) + Sigma(N)(k=1) a(jk)x(k)) + x(j)Psi(x(1), ..., x(N)), j = 1, ..., N, where a(j), and a(jk) are constants for j, k = 1, ..., N and Psi(x(1), ..., x(N)) is a homogeneouspolynomial of degree n > 2, with either one additional invariant hyperplane, or with one exponential factor. We also study the integrability of the N-dimensional classical Lotka-Volterra systems (when Psi(x(1), ..., x(N)) = 0). In particular we consider the integrability of the asymmetric May-Leonard systems. (C) 2020 Elsevier Inc. All rights reserved.