Dynamical Response of a Van der Pol System with an External Harmonic Excitation and Fractional Derivative

DOI10.1007/978-3-319-01411-1_6zbMath1335.34022OpenAlexW1645740390MaRDI QIDQ5261476

Grzegorz Litak, Arkadiusz Syta

Publication date: 3 July 2015

Published in: Discontinuity and Complexity in Nonlinear Physical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-01411-1_6

zbMATH Keywords

fractional derivative0-1 testchaos detectionvan der Pol system

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Relaxation oscillations for ordinary differential equations (34C26) Fractional ordinary differential equations (34A08)

Cites Work

• Analysis of a fractional order Van der Pol-like oscillator via describing function method
• Some applications of fractional calculus in engineering
• Chaos in limit cycle systems with external periodic excitations
• Nonlinear vibrations of fractionally damped systems
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Chaos in the fractional order periodically forced complex Duffing's oscillators
• A pair of van der Pol oscillators coupled by fractional derivatives
• Chaotic dynamics of the fractionally damped Duffing equation
• Nonlinear differential equations with fractional damping with applications to the 1dof and 2dof pendulum
• Testing for chaos in deterministic systems with noise
• A new test for chaos in deterministic systems
• Transition to chaos in a generalized van der Pol's equation
• VIBRATION ANALYSIS OF A SELF-EXCITED SYSTEM WITH PARAMETRIC FORCING AND NONLINEAR STIFFNESS
• Application of the 0-1 Test for Chaos to Experimental Data

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