Work

On the Dynamics of a Modified van der Pol–Duffing Oscillator

Year: 2025

Type: article

Abstract: The 3-dimensional modified van der Pol–Duffing oscillator has been studied by several authors. We complete its study, first characterizing its zero-Hopf equilibria and then its zero-Hopf bifurcations—i.e., we provide sufficient conditions for the existence of three, two or one periodic solutions, bifurcating from the zero-Hopf equilibrium localized at the origin of coordinates. Recall that an equilibrium point of a 3-dimensional differential system whose eigenvalues are zero and a pair of purely imaginary eigenvalues is a zero-Hopf equilibrium. Finally, we determine the dynamics of this system near infinity, i.e., we control the orbits that escape to or come from the infinity.

Source: Axioms

DOI: 10.3390/axioms14040321

Authors: Oscar A. R. Cespedes, Jaume Llibre

Institutions: Universidad Distrital Francisco José de Caldas, Universitat Autònoma de Barcelona

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Agència de Gestió d'Ajuts Universitaris i de Recerca