First Integrals of the May–Leonard Asymmetric System

Valery Antonov, Wilker Fernandes, Valery Romanovski, Natalie Shcheglova
2019 Mathematics  
For the May–Leonard asymmetric system, which is a quadratic system of the Lotka–Volterra type depending on six parameters, we first look for subfamilies admitting invariant algebraic surfaces of degree two. Then for some such subfamilies we construct first integrals of the Darboux type, identifying the systems with one first integral or with two independent first integrals.
doi:10.3390/math7030292 fatcat:v2ccizuqqjemvcndcftch7b5hm