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

Author(s)

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

• Document type: Journal article
• Source: CHAOS SOLITONS & FRACTALS; v. 175, p. 9-pg., 2023-08-19.

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-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. (AU)

• FAPESP's process: 22/14484-9 - Applications in biology of piecewise differential equations
• Grantee: Leonardo Pereira Costa da Cruz
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 20/04717-0 - Dynamical systems with symmetries and implicit differential equations
• Grantee: Luiz Fernando da Silva Gouveia
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 21/14987-8 - Bifurcation of limit cycles in smooth piecewise systems and an application in Medicine
• Grantee: Leonardo Pereira Costa da Cruz
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 22/03800-7 - Study of math epidemiological models in piecewise smooth systems and regularization
• Grantee: Yagor Romano Carvalho
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 21/14695-7 - Limit cycles, regularization and period function of piecewise smooth planar systems.
• Grantee: Yagor Romano Carvalho
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 22/03801-3 - Lower bounds for local cyclicity for Kolmogorov systems on planar piecewise vector fields
• Grantee: Luiz Fernando da Silva Gouveia
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor