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

Yagor Romano Carvalho, Leonardo P.C. Da Cruz and Luiz F.S. Gouveia

Chaos, Solitons & Fractals, 2023, vol. 175, issue P1

Abstract: 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.

Keywords: Center-focus; Cyclicity; Limit cycles; Weak-focus order; Lyapunov quantities; Lotka–Volterra systems; Kolmogorov systems (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:175:y:2023:i:p1:s096007792300838x

DOI: 10.1016/j.chaos.2023.113937

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