The integrability of a class of cubic Lotka–Volterra systems

The integrability of a class of cubic Lotka–Volterra systems ẋ=x(1−a0x2−a1xy−a2y2),ẏ=y(−λ+b0x2+b1xy+b2y2), is studied. For odd λλ satisfying λ≥3λ≥3, we derive the necessary and sufficient conditions for the integrabilities of the above systems.