Analysis of a fractional order Van der Pol-like oscillator via describing function method

DOI10.1007/s11071-009-9647-0zbMath1204.70018OpenAlexW2093720082MaRDI QIDQ623881

Mohammad Saleh Tavazoei, Mina Attari, Mohammad Haeri

Publication date: 8 February 2011

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-009-9647-0

zbMATH Keywords

harmonic balancefractional Van der Pol oscillatordescribing function methodoscillatory parametric region

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Fractional ordinary differential equations (34A08)

Related Items (17)

Numerical scheme and dynamic analysis for variable-order fractional van der Pol model of nonlinear economic cycle ⋮ Models and numerical schemes for generalized van der Pol equations ⋮ On multiple limit cycles in sliding-mode control systems via a generalized describing function approach ⋮ Static feedback versus fractionality of the electrical elements in the van der Pol circuit ⋮ Limit cycle oscillations in a mechanical system under fractional-order Liénard type nonlinear feedback ⋮ On the existence of periodic solutions in time-invariant fractional order systems ⋮ Formulation and solution to time-fractional generalized Korteweg-de Vries equation via variational methods ⋮ Approximate expressions of a fractional order Van der Pol oscillator by the residue harmonic balance method ⋮ Limit cycle prediction of systems with fractional controllers and backlash ⋮ NEIMARK BIFURCATIONS OF A GENERALIZED DUFFING–VAN DER POL OSCILLATOR WITH NONLINEAR FRACTIONAL ORDER DAMPING ⋮ TRANSITION CURVES AND BIFURCATIONS OF A CLASS OF FRACTIONAL MATHIEU-TYPE EQUATIONS ⋮ Synchronization for a class of uncertain fractional order chaotic systems with unknown parameters using a robust adaptive sliding mode controller ⋮ Asymptotic limit cycle of fractional van der Pol oscillator by homotopy analysis method and memory-free principle ⋮ Chaos synchronization in fractional differential systems ⋮ Time-fractional KdV equation: Formulation and solution using variational methods ⋮ Analytical solutions of nonlinear system of fractional-order van der Pol equations ⋮ Dynamical Response of a Van der Pol System with an External Harmonic Excitation and Fractional Derivative

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