Oscillatory region and asymptotic solution of fractional van der Pol oscillator via residue harmonic balance technique

DOI10.1016/J.APM.2011.02.007zbMath1221.34011OpenAlexW2017421888MaRDI QIDQ639162

Zhongjin Guo, Hong-Xiang Yang, Andrew Y. T. Leung

Publication date: 18 September 2011

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2011.02.007

zbMATH Keywords

residue harmonic balancefractional van der Pol oscillatoroscillatory region

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Fractional ordinary differential equations (34A08)

Related Items (10)

TRANSITION CURVES AND BIFURCATIONS OF A CLASS OF FRACTIONAL MATHIEU-TYPE EQUATIONS ⋮ Approximate limit cycles of coupled nonlinear oscillators with fractional derivatives ⋮ EFFECTS OF FRACTIONAL DIFFERENTIATION ORDERS ON A COUPLED DUFFING CIRCUIT ⋮ Bifurcating periodic solution for a class of first-order nonlinear delay differential equation after Hopf bifurcation ⋮ Stochastic response of dynamical systems with fractional derivative term under wide-band excitation ⋮ Asymptotic limit cycle of fractional van der Pol oscillator by homotopy analysis method and memory-free principle ⋮ Free vibration analysis of a structural system with a pair of irrational nonlinearities ⋮ On oscillatory and nonoscillatory behavior of solutions for a class of fractionalorder differential equations ⋮ Analytical solutions of nonlinear system of fractional-order van der Pol equations ⋮ THE REPRODUCING KERNEL ALGORITHM FOR NUMERICAL SOLUTION OF VAN DER POL DAMPING MODEL IN VIEW OF THE ATANGANA–BALEANU FRACTIONAL APPROACH

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• NUMERICAL SOLUTIONS OF SECOND ORDER IMPLICIT NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS
• Analysis of the Van der Pol Oscillator Containing Derivatives of Fractional Order

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