Zero-Hopf bifurcation in a 3D jerk system

Author(s)

Braun, Francisco ^[1] ; Mereu, Ana C. ^[2]

Affiliation

^[1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

^[2] Univ Fed Sao Carlos, Dept Fis Quim & Matemat, BR-18052780 Sorocaba, SP - Brazil

• Document type: Journal article
• Source: NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS; v. 59, JUN 2021.
• Web of Science Citations: 0

Abstract

Let the three-dimensional differential system defined by the jerk equation (x) over dot = a(x) over dot +x(x) over dot(2) -x(3)-bx+c(x) over dot, with a, b, c is an element of R. When a = b = 0 and c < 0 the equilibrium point localized at the origin of coordinates is a zero-Hopf equilibrium. We analyse the zero-Hopf bifurcation occurring at this singular point after persuading a quadratic perturbation of the coefficients. Particularly, by using averaging theory of second order, we prove that up to three periodic orbits born as the parameter of the perturbation tends to zero. (C) 2020 Elsevier Ltd. All rights reserved. (AU)

• FAPESP's process: 18/13481-0 - Geometry of control, dynamical and stochastic systems
• Grantee: Marco Antônio Teixeira
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 17/00136-0 - Global injectivity of maps in R^n
• Grantee: Francisco Braun
• Support Opportunities: Regular Research Grants