scholarly journals Discretization of forced Duffing system with fractional-order damping

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Ahmed MA El-Sayed ◽  
Zaki FE El-Raheem ◽  
Sanaa M Salman
Keyword(s):  
Fractional Order ◽  
Duffing System

Superharmonic Resonance of Fractional-Order Mathieu–Duffing Oscillator

2019 ◽  
Vol 14 (7) ◽  
Author(s):  
Jiangchuan Niu ◽  
Xiaofeng Li ◽  
Haijun Xing
Keyword(s):  
Fractional Order ◽  
Order Term ◽  
Duffing Oscillator ◽  
Steady State Solution ◽  
Harmonic Excitation ◽  
Frequency Equation ◽  
Superharmonic Resonance ◽  
Duffing System ◽  
Resonance Response ◽  
Kbm Method

The superharmonic resonance of fractional-order Mathieu–Duffing oscillator subjected to external harmonic excitation is investigated. Based on the Krylov–Bogolubov–Mitropolsky (KBM) asymptotic method, the approximate analytical solution for the third superharmonic resonance under parametric-forced joint resonance is obtained, where the unified expressions of the fractional-order term with fractional order from 0 to 2 are gained. The amplitude–frequency equation for steady-state solution and corresponding stability condition are also presented. The correctness of the approximate analytical results is verified by numerical results. The effects of the fractional-order term, excitation amplitudes, and nonlinear stiffness coefficient on the superharmonic resonance response of the system are analyzed in detail. The results show that the KBM method is effective to analyze dynamic response in a fractional-order Mathieu–Duffing system.

Chaos in a fractional order modified Duffing system

2007 ◽  
Vol 34 (2) ◽  
pp. 262-291 ◽  
Author(s):  
Zheng-Ming Ge ◽  
Chan-Yi Ou
Keyword(s):  
Fractional Order ◽  
Duffing System

Nonlinear Dynamics of Duffing System With Fractional Order Damping

2009 ◽  
Author(s):  
Junyi Cao ◽  
Chengbin Ma ◽  
Hang Xie ◽  
Zhuangde Jiang
Keyword(s):  
Nonlinear Dynamics ◽  
Fractional Order ◽  
Period Doubling ◽  
Excitation Amplitude ◽  
Bifurcation Diagrams ◽  
Duffing System ◽  
Runge Kutta Method ◽  
Route To Chaos ◽  
Euler Methods ◽  
Period Motion

In this paper, nonlinear dynamics of Duffing system with fractional order damping is investigated. The four order Runge-Kutta 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 also used to exam the effects of excitation amplitude and frequency on Duffing system with fractional order damping. The analysis results show that the fractional order damped Duffing system exhibits period motion, chaos, period motion, chaos, period motion in turn when the fractional order changes from 0.1 to 2.0. A period doubling route to chaos is clearly observed.

scholarly journals Sequential Parameter Identification of Fractional-Order Duffing System Based on Differential Evolution Algorithm

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Li Lai ◽  
Yuan-Dong Ji ◽  
Su-Chuan Zhong ◽  
Lu Zhang
Keyword(s):  
Differential Evolution ◽  
Parameter Identification ◽  
Fractional Order ◽  
Dynamic Properties ◽  
Differential Evolution Algorithm ◽  
Duffing System ◽  
Identification Method ◽  
System A ◽  
Evolution Algorithm ◽  
Search Capability

Using the dynamic properties of fractional-order Duffing system, a sequential parameter identification method based on differential evolution optimization algorithm is proposed for the fractional-order Duffing system. Due to the step by step parameter identification method, the dimension of parameter identification of each step is greatly reduced and the search capability of the differential evolution algorithm has been greatly improved. The simulation results show that the proposed method has higher convergence reliability and accuracy of identification and also has high robustness in the presence of measurement noise.

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