Work

Hopf bifurcation in Kolmogorov systems of degree 4 in R2 and R3

Year: 2025

Type: article

Abstract: We consider the Kolmogorov system of degree 4 in R2 having an equilibrium point in the positive quadrant and the Kolmogorov system of degree 4 in R3 having an equilibrium point in the positive octant. Note that from a biological point of view the two equilibria considered must be in the positive quadrant and octant. We give the conditions under which the equilibrium points of the planar and spatial systems will be a Hopf point and a zero-Hopf point, respectively. The explicit conditions for the existence of limit cycles bifurcating from these two equilibria are obtained using the averaging theory. Moreover, we characterize the stability or instability of these limit cycles.

Source: Journal of Mathematical Physics

DOI: 10.1063/5.0275638

Authors: J. Llibre, Y. P. Mancilla-Martínez

Institutions: Universitat Autònoma de Barcelona, University of Bío-Bío

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green