کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1139218 1489425 2013 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Approximate expressions of a fractional order Van der Pol oscillator by the residue harmonic balance method
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی کنترل و سیستم های مهندسی
پیش نمایش صفحه اول مقاله
Approximate expressions of a fractional order Van der Pol oscillator by the residue harmonic balance method
چکیده انگلیسی

Although the Van der Pol oscillator, which was originally proposed as a model of vacuum tube circuits, has been widely used in electronics, biology and acoustics, its characteristics in fractional order formulations are not clearly explained even now. This paper is interested in gaining insights of approximate expressions of the periodic solutions in a fractional order Van der Pol oscillator. The presence of fractional derivatives requires the use of suitable criteria, which usually makes the analytical work much hard. Most existing methods for studying the nonlinear dynamics fail when applied to such a class of fractional order systems. In this paper, based on the residue harmonic balance method, a detailed analysis on approximations to the periodic oscillations of the fractional order Van der Pol equation is investigated. The relations that express the frequency and amplitude of the generated oscillations as functions of the orders and parameters are shown. Moreover, some examples are provided for comparing approximations with numerical solutions of the periodic oscillations. Numerical results reveal that the residue harmonic balance method is very effective for obtaining approximate solutions of fractional oscillations.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Mathematics and Computers in Simulation - Volume 89, March 2013, Pages 1–12
نویسندگان
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