Integrability and linearizability of the Lotka–Volterra systems

Integrability and linearizability of the Lotka– Volterra systems are studied. We prove sufficient conditions for integrable but not linearizable systems for any rational resonance ratio. We give new sufficient conditions for linearizable Lotka–Volterra systems. Sufficient conditions for integrable Lotka– Volterra systems with 3:q resonance are given. In the particular cases of 3:5 and 3:4 resonances, necessary and sufficient conditions for integrable systems are given.