New lower bound for the Hilbert number in low degree Kolmogorov systems
Romano Carvalho, Yagor (Universidade de São Paulo)
Da Cruz, Leonardo Pereira Costa (Universidade de São Paulo)
Gouveia, Luiz Fernando (Universidade Estadual Paulista "Júlio de Mesquita Filho")

Date:	2023
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 M(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 (3) ≥ 6. In addition, we obtain new lower bounds for M (n) proving that M (4) ≥ 13 and M (5) ≥ 22.
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Center-focus ; Cyclicity ; Limit cycles ; Weak-focus order ; Lyapunov quantities ; Lotka-Volterra Systems ; Kolmogorov Systems
Published in:	Chaos, solitons and fractals, Vol. 175, Num. Part 1 (October 2023) , art. 113937, ISSN 0960-0779

DOI: 10.1016/j.chaos.2023.113937

Postprint 18 p, 2.8 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
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