New lower bound for the Hilbert number in low degree Kolmogorov systems

Our main goal in this paper is to study the number of small-amplitude isolated periodic orbits, so-called limit cycles, surrounding only one equilibrium point a class of polynomial Kolmogorov systems. We denote by M-K (n) the maximum number of limit cycles bifurcating from the equilibrium point via a degenerate Hopf bifurcation for a polynomial Kolmogorov vector field of degree n. In this work, we obtain another example such that M-K (3) >= 6. In addition, we obtain new lower bounds for M-K (n) proving that M-K (4) >= 13 and M-K (5) >= 22.