Global study of Rayleigh–Duffing oscillators. (8th March 2016)

• Record Type: Journal Article
• Authors: Chen, Hebai; Zou, Lan
• Is Part Of: Journal of physics. Volume 49:Number 16(2016)
• Publication Date: 2016-03-08
• Subjects: Rayleigh–Duffing oscillator -- homoclinic loop -- bifurcation diagram -- limit cycle -- gluing bifurcation; 34C07 -- 34C23 -- 34C37 -- 34K18; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/49/16/165202
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: In this paper we investigate the global dynamics of Rayleigh–Duffing oscillators with global parameters, including equilibria at both finity and infinity, existences and coexistence of limit cycles and homoclinic loops. In fact, this oscillator will occur Hopf bifurcations, homoclinic bifurcations and double limit cycle bifurcations. Moreover, we find that the homoclinic bifurcation of this oscillator is special which is a gluing bifurcation. The global bifurcation diagram and all phase portrait are given, and numerical simulations are shown to verify our analysis finally.