FRACTIONAL DUFFING'S EQUATION AND GEOMETRICAL RESONANCE-Reference-Cited by-同舟云学术

FRACTIONAL DUFFING'S EQUATION AND GEOMETRICAL RESONANCE

Published:2013-05 Issue:05 Volume:23 Page:1350089
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

JIMÉNEZ S.¹,GONZÁLEZ J. A.²,VÁZQUEZ L.³

Affiliation:

1. Departamento de Matemática Aplicada a las TT.II., E.T.S.I.T., Universidad Politécnica de Madrid, Avenida Complutense 30, 28040 Madrid, Spain

2. Centro de Física, Instituto Venezolano de Investigaciones Científicas, Apartado Postal 21827, Caracas 1020-A, Venezuela

3. Departamento de Matemática Aplicada, Facultad de Informática, Universidad Complutense de Madrid, Calle Profesor José García Santesmases, s/n, 28040 Madrid, Spain

Abstract

We investigate the Fractional Duffing equation in the presence of nonharmonic external perturbations. We have applied the concept of Geometrical Resonance to this equation. We have obtained the conditions that should be satisfied by the external driving forces in order to produce high-amplitude periodic oscillations avoiding chaos. We also show that, for Duffing's equation with fractional damping, the perturbations that satisfy the Geometrical Resonance conditions are nonperiodic functions.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127413500892

Reference21 articles.

1. The Control of Chaos: Theoretical Schemes and Experimental Realizations

2. The synchronization of chaotic systems

3. Geometrical Resonance as a Chaos Eliminating Mechanism

4. Maintenance and Suppression of Chaos by Weak Harmonic Perturbations: A Unified View

5. Algorithms for the fractional calculus: A selection of numerical methods

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