Darboux integrability of a Mathieu-van der Pol-Duffing oscillator. (April 2023)

• Record Type: Journal Article
• Authors: Cen, Zhihao; Xie, Feng
• Is Part Of: Nonlinear analysis. Volume 70(2023)
• Publication Date: 2023-04
• Subjects: Darboux polynomials -- Darboux first integrals -- Mathieu-van der Pol-Duffing oscillator; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103785
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we characterize all the Darboux polynomials of a Mathieu-van der Pol-Duffing oscillator by transforming from the original system into a three dimensional system. We also provide a complete classification of the rational first integrals and of the Darboux first integrals through the analysis of its Darboux polynomials and its exponential factors.