New lower bound for the Hilbert number in low degree Kolmogorov systems
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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 MK(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 MK(3)≥6. In addition, we obtain new lower bounds for MK(n) proving that MK(4)≥13 and MK(5)≥22.
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Center-focus, Cyclicity, Kolmogorov systems, Limit cycles, Lotka–Volterra systems, Lyapunov quantities, Weak-focus order
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Chaos, Solitons and Fractals, v. 175.
