Periodic orbits bifurcating from a Hopf equilibrium of 2-dimensional polynomial Kolmogorov systems of arbitrary degree

A Hopf equilibrium of a differential system in $R^2$ is an equilibrium point whose linear part has eigenvalues $\pm \omega i$ with $\omega \ne 0,$ where $i=\sqrt{-1}$. We provide necessary and sufficient conditions for the existence of a limit cycle bifurcating from a Hopf equilibrium of 2–dimensional polynomial Kolmogorov systems of arbitrary degree. We provide an estimation of the bifurcating small limit cycle and also characterize the stability of this limit cycle.