Work

Stability and Bifurcations in Time-Delay Systems: A Novel and Efficient Blend of Methods

Year: 2024

Type: article

Abstract: The goal of this paper is to introduce a hybrid technique, combining two existing methods conveniently, to analyze the stability and bifurcations of equilibrium points and periodic orbits in delay-differential equations of retarded type. One method is called the frequency-domain approach, an analytical tool based on control theory allowing to detect and represent periodic solutions emerging from the Hopf bifurcations, via Fourier series and harmonic balances. The second one, the so-called semi-discretization method, provides a numerical scheme to approximate the monodromy operator of a periodic solution, thus permitting to establish the stability and bifurcations of limit cycles as well as analyzing the equilibrium points. It is shown that a proper combination of these methods provides a straightforward strategy to study both local and global bifurcations in time-delay systems. The usefulness of the proposed approach is shown by three examples, where the results are compared with those given by the software DDE-BIFTOOL.

Source: International Journal of Bifurcation and Chaos

DOI: 10.1142/s0218127424501955

Authors: Griselda R. Itovich, Franco S. Gentile, Jorge L. Moiola

Institutions: National University of Río Negro, Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Científico Tecnológico - Bahía Blanca, Universidad Nacional del Sur

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Universidad Nacional del Sur, Universidad Nacional de Río Negro

Awards: G5579167290, G5618948084, G7262506589