Integrability and non-linearizability of weak saddles in a cubic Kolmogorov model

Abstract This paper is devoted to the integrability and non-linearizability for a cubic Kolmogorov system with three positive equilibria. The necessary and sufficient conditions for each positive equilibrium to be an integrable saddle are given. Furthermore, by careful computation of period constants, we can see that period constant of certain order does not vanish. Therefore, we arrive to the conclusion that the system is not linearizable at the three positive equilibria.