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An analytical approach to investigate the response and stability of Van der Pol–Mathieu–Duffing oscillators under different excitation functions
Author(s) -
Kimiaeifar A.
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1269
Subject(s) - van der pol oscillator , mathematics , duffing equation , homotopy analysis method , stability (learning theory) , excitation , mathieu function , mathematical analysis , nonlinear system , chaotic , expression (computer science) , range (aeronautics) , homotopy , physics , quantum mechanics , pure mathematics , computer science , materials science , artificial intelligence , composite material , programming language , machine learning
In this paper the chaotic behavior of Van der Pol–Mathieu–Duffing oscillator under different excitation functions is studied. Governing equation is solved analytically using a powerful kind of analytic technique for nonlinear problems, namely the ‘homotopy analysis method’, for the first time. Present solution gives an expression, which can be used in a wide range of time for all domain of response. Comparisons of the obtained solutions with numerical results show that this method is effective and convenient for solving this problem. Finally, by using obtained analytical solution the stability and response of system under different excitation functions and constant parameters are shown. Copyright © 2010 John Wiley & Sons, Ltd.