{"title":"Global dynamics of a generalized arbitrary order Van der Pol–Duffing Oscillator","authors":"Jueliang Zhou , Lan Zou","doi":"10.1016/j.cnsns.2024.108445","DOIUrl":null,"url":null,"abstract":"<div><div>We study the global bifurcation diagram and corresponding global phase portraits in the Poincaré disc for a generalized van der Pol-Duffing oscillator, which has four nonlinear terms with arbitrary orders. This nonlinear oscillator possesses more diverse and complicated dynamical behaviours, including the heteroclinic bifurcation, generalized Hopf bifurcation and pitchfork bifurcation. Moreover, theoretical results are exhibited via numerical simulations.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"140 ","pages":"Article 108445"},"PeriodicalIF":3.4000,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570424006300","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We study the global bifurcation diagram and corresponding global phase portraits in the Poincaré disc for a generalized van der Pol-Duffing oscillator, which has four nonlinear terms with arbitrary orders. This nonlinear oscillator possesses more diverse and complicated dynamical behaviours, including the heteroclinic bifurcation, generalized Hopf bifurcation and pitchfork bifurcation. Moreover, theoretical results are exhibited via numerical simulations.
期刊介绍：
The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity.
The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged.
Topics of interest:
Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity.
No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.
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