Sufficient conditions for the existence of periodic solutions of the extended Duffing-Van der Pol oscillator

Author(s)

Euzebio, Rodrigo D. ^{[1, 2]} ; Llibre, Jaume ^[1]

Affiliation

^[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain

^[2] UNESP, IBILCE, Dept Matemat, Rua Cristovao Colombo 2265, BR-1505400 Sao Jose De Rio Preto, SP - Brazil

• Document type: Journal article
• Source: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS; v. 93, n. 8, p. 1358-1382, 2016.
• Web of Science Citations: 1

Abstract

In this paper, some aspects on the periodic solutions of the extended Duffing-Van der Pol oscillator are discussed. Doing different rescaling of the variables and parameters of the system associated with the extended Duffing-Van der Pol oscillator, we show that it can bifurcate one or three periodic solutions from a two-dimensional manifold filled by periodic solutions of the referred system. For each rescaling we exhibit concrete values for which these bounds are reached. Beyond that we characterize the stability of some periodic solutions. Our approach is analytical and the results are obtained using the averaging theory and some algebraic techniques. (AU)

• FAPESP's process: 10/18015-6 - A study for minimal sets in non-smooth systems in dimensions two and three
• Grantee: Rodrigo Donizete Euzébio
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 13/25828-1 - Minimal sets and invariant manifolds in piecewise smooth systems
• Grantee: Rodrigo Donizete Euzébio
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 12/05635-1 - Study of families of periodic orbits and their bifurcations in differential equations of finite dimension
• Grantee: Rodrigo Donizete Euzébio
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate