The analytic integrability problem for perturbations of homogeneous quadratic Lotka-Volterra systems

Abstract

We solve the analytic integrability problem for diferential systems in the plane whose origin is an isolated singularity and the first homogeneous component is a quadratic Lotka-Volterra type. As an application, we give the analytically integrable systems of a class of systems $\dot{x}=x(P1+P2)$; $\dot{y}=y(Q1+Q2)$; being Pi,Qi homogeneous polynomials of degree i.

Cited by in corpus (1)

• Integrability and linearizability conditions for a cubic Lotka-Volterra systems