Darboux integrability of a Mathieu-van der Pol-Duffing oscillator
type: Item
instance of: scholarly article
title: Darboux integrability of a Mathieu-van der Pol-Duffing oscillator
author: Zhihao Cen
author: Feng Xie
published in: Nonlinear Analysis. Real World Applications
publication date: 2023-01-11T00:00:00Z
review text: In this paper, the author studied the Darboux integrability of a three-dimensional system of ordinary differential systems \[ \dot{x}=y,~~\dot{y}=mx+\alpha y+\chi z-\gamma x^3-\beta x^2y,~~\dot{z}=-ky+\bar{n}z \] which describes the Mathieu-van der Pol-Duffing oscillator coupled to an electrical circuit by a piezoelectric device. They provided a complete classification of Darboux polynomials of this model, which yields all possible rational or Darboux first integrals. The method is based on the careful analysis of the polynomial solution of a linear partial differential equation, which may be used to deal with Darboux integrability of other simialr models.
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34B30
zbMATH DE Number: 7640619
zbMATH Keywords: Darboux Polynomials
zbMATH Keywords: Darboux first integrals
zbMATH Keywords: Mathieu-van der Pol-Duffing oscillator
reviewed by: Kaiyin Huang
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2022.103785
OpenAlex ID: W4308487044
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DOI: 10.1016/J.NONRWA.2022.103785
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description: scientific article; zbMATH DE number 7640619