Solution of the Duffing-van der Pol oscillator equation by a differential transform method

Mukherjee S.; Roy B.; Dutta S.

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Solution of the Duffing-van der Pol oscillator equation by a differential transform method

机译：用微分变换法求解Duffing-van der Pol振荡器方程

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In this paper, we have tried to implement a relatively new exact series method of solution, known as the differential transform method, for solving one of the widely studied and challenging equations in nonlinear dynamics, the Duffing-van der Pol oscillator equation. Chandrasekar et al (2004 J. Phys. A 37 4527) showed that the force-free Duffing-van der Pol oscillator is completely integrable for a specific parametric choice, and they derived a general solution for this parametric choice. The results of this paper are in sufficient agreement with those of Chandrasekar et al.

机译：在本文中，我们试图实现一种相对较新的精确级数解方法，称为微分变换方法，以解决非线性动力学中广泛研究且具有挑战性的方程式Duffing-van der Pol振动器方程。 Chandrasekar等人（2004 J. Phys。A 37 4527）表明，对于特定的参数选择，无力的Duffing-van der Pol振荡器是完全可积分的，他们推导了此参数选择的一般解决方案。本文的结果与Chandrasekar等人的研究结果充分吻合。

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《Physica Scripta: An International Journal for Experimental and Theoretical Physics》 |2011年第1期|共4页
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Mukherjee S.; Roy B.; Dutta S.;
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中图分类物理学;
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1. Solution of the Duffing-van der Pol oscillator equation by a differential transform method [J] . Mukherjee S., Roy B., Dutta S. Physica Scripta: An International Journal for Experimental and Theoretical Physics . 2011,第1期

机译：用微分变换法求解Duffing-van der Pol振荡器方程
2. Reply to Comment on 'Solution of the Duffing-van der Pol oscillator equation by the differential transform method' [J] . Mukherjee S. Physica Scripta: An International Journal for Experimental and Theoretical Physics . 2011,第3期

机译：对“用微分变换法求解Duffing-van der Pol振荡器方程的评论”的评论
3. Comment on 'Solution of the Duffing-van der Pol oscillator equation by a differential transform method' [J] . Fernndez F.M. Physica Scripta: An International Journal for Experimental and Theoretical Physics . 2011,第3期

机译：评论“用差分变换法求解Duffing-van der Pol振荡器方程”
4. Asymptotic Analytical Solutions of a Two Coupled Duffing-Van Der Pol Oscillators Using the Extended Homotopy Analysis Method [C] . Sheng-min Chen, Chun-mei Duan International Conference on Industrial Control and Electronics Engineering;ICICEE 2012 . 2012

机译：使用扩展的同伦分析方法的两对Duffing-Van Der Pol振动器的渐近解析解
5. The first-integral method for Duffing-van der Pol-type oscillator system [D] . Hu, Xiaochuan 2011

机译：Duffing-van der Pol型振荡器系统的第一积分方法
6. A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations [O] . Brahim Benhammouda, Hector Vazquez-Leal -1

机译：微分变换方法的一种新的多步技术用于求解某些非线性可变时滞微分方程的解析解
7. Solutions of the Force-Free Duffing-van der Pol Oscillator Equation [O] . Najeeb Alam Khan, Muhammad Jamil, Syed Anwar Ali, 2011

机译：无动力Duffing-van der振荡器方程的解决方案

Solution of the Duffing-van der Pol oscillator equation by a differential transform method

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