Integrability and bifurcations of limit cycles in a cubic Kolmogorov system

摘要

We investigate the planar cubic Kolmogorov systems with three invariant algebraic curves which have a equilibrium at (1,1). With the help of computer algebra system MATHEMATICA, we prove that five limit cycles can be bifurcated from a critical point in the first quadrant. Moreover, the necessary conditions of center are obtained, by technical transformation, and its sufficiencies are proved.