Resonance oscillation and transition to chaos in \(\phi^8\)-Duffing-van der Pol oscillator
type: Item
instance of: scholarly article
title: Resonance oscillation and transition to chaos in \(\phi^8\)-Duffing-van der Pol oscillator
zbMATH Open document ID: 1500.34034
author: A. O. Adelakun
published in: International Journal of Applied and Computational Mathematics
publication date: 2022-03-15T00:00:00Z
review text: Following the study of a Duffing-Van der Pol oscillator of which the potential function is a polynomial of degree six, the author extend his investigation of the oscillator to the potential function of degree eight. It seems that the new system exhibits much richer nonlinear behavior than the previous one. From numerical simulations, even though the system with degree six is stable, a small value of the coefficient of the degree-eight term already induces very complex dynamical behavior such as the coexistence of multiple limit cycles, period-doubling route to chaos and sudden chaos. An electronic circuit was also designed to confirm to a great extent the theoretical and simulation results.
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 94C60
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34B30
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 34D08
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 7490013
zbMATH Keywords: hidden dynamics
zbMATH Keywords: \( \phi^8\)-DVP oscillator
zbMATH Keywords: resonance oscillation
zbMATH Keywords: bifurcation structures
zbMATH Keywords: unstable states
reviewed by: Kwok-wai Chung
MaRDI profile type: Publication
full work available at URL: s40819-021-01005-6
OpenAlex ID: W3171410359
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DOI: 10.1007/S40819-021-01005-6
description: scientific article; zbMATH DE number 7490013