广义任意阶范德尔波尔-杜芬振荡器的全局动力学

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-11-16 DOI:10.1016/j.cnsns.2024.108445

Jueliang Zhou , Lan Zou

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引用次数: 0

摘要

我们研究了具有任意阶数的四个非线性项的广义范德波尔-杜芬振荡器在波因卡雷圆盘中的全局分岔图和相应的全局相位图。这种非线性振荡器具有更多样、更复杂的动力学行为，包括异折线分岔、广义霍普夫分岔和叉形分岔。此外，还通过数值模拟展示了理论结果。

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Global dynamics of a generalized arbitrary order Van der Pol–Duffing Oscillator

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.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

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.