Discretization of forced Duffing system with fractional-order damping
نویسندگان
چکیده
منابع مشابه
Nonlinear Dynamics of Duffing System with Fractional Order Damping
In this paper, nonlinear dynamics of Duffing system with fractional order damping is investigated. The four order RungeKutta method and ten order CFE-Euler methods are introduced to simulate the fractional order Duffing equations. The effect of taking fractional order on the system dynamics is investigated using phase diagrams, bifurcation diagrams and Poincare map. The bifurcation diagram is a...
متن کاملThree Solutions for Forced Duffing-Type Equations with Damping Term
Correspondence should be addressed to Yongkun Li, [email protected] Received 16 December 2010; Revised 6 February 2011; Accepted 11 February 2011 Academic Editor: Dumitru Motreanu Copyright q 2011 Y. Li and T. Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the...
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This paper introduces a numerical technique for the estimation of stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise excitation. The Wiener-Hermite expansion is integrated with the Grunwald-Letnikov approximation in case of fractional order damping and with Coimbra approximation in case of variableorder damping. The numerical solver...
متن کاملVibration of the Duffing Oscillator: Effect of Fractional Damping
We have applied the Melnikov criterion to examine a global homoclinic bifurcation and transition to chaos in a case of the Duffing system with nonlinear fractional damping and external excitation. Using perturbation methods we have found a critical forcing amplitude above which the system may behave chaotically. The results have been verified by numerical simulations using standard nonlinear to...
متن کاملForced harmonic vibration of a Duffing oscillator with linear viscous damping
TheDuffing oscillator has become a classical paradigm for illustrating the remarkable jump phenomenon and other nonlinear behaviour [1,2]. The understanding gained on the basis of this low-order nonlinear systemhas helped in the development of reducedorder models of complex mechanical systems ranging from microscales to macroscales [3,4]. The nondimensional Duffing equation with damping and ext...
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2014
ISSN: 1687-1847
DOI: 10.1186/1687-1847-2014-66