Three-Dimensional Lotka–Volterra Systems with 3:−1:2-Resonance

We study the local integrability at the origin of a nine-parameter family of three-dimensional Lotka–Volterra differential systems with (3:− 1:2)-resonance. We give necessary and sufficient conditions on the parameters of the family that guarantee the existence of two independent local first integrals at the origin of coordinates. Additionally, we classify those cases where the origin is linearizable.