© 2017 the authors. We go beyond in the study of the integrability of the classical model of competition between three species studied by May and Leonard , by considering a more realistic asymmetric model. Our results show that there are no global analytic first integrals and we provide all proper rational first integrals of this extended model by classifying its invariant algebraic surfaces.
- analytic integrability
- asymmetric Lotka-Volterra systems
- polynomial integrability
- rational integrability