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Stability of Fractional Order System of Duffing Equation with Quadratic and Cubic Nonlinearities

A. George Maria Selvam1 , D. Vignesh2 , R. Janagaraj3

Section:Research Paper, Product Type: Journal Paper
Volume-07 , Issue-05 , Page no. 16-19, Mar-2019

CrossRef-DOI:   https://doi.org/10.26438/ijcse/v7si5.1619

Online published on Mar 10, 2019

Copyright © A. George Maria Selvam, D. Vignesh, R. Janagaraj . 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 original work is properly cited.

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IEEE Style Citation: A. George Maria Selvam, D. Vignesh, R. Janagaraj, “Stability of Fractional Order System of Duffing Equation with Quadratic and Cubic Nonlinearities,” International Journal of Computer Sciences and Engineering, Vol.07, Issue.05, pp.16-19, 2019.

MLA Style Citation: A. George Maria Selvam, D. Vignesh, R. Janagaraj "Stability of Fractional Order System of Duffing Equation with Quadratic and Cubic Nonlinearities." International Journal of Computer Sciences and Engineering 07.05 (2019): 16-19.

APA Style Citation: A. George Maria Selvam, D. Vignesh, R. Janagaraj, (2019). Stability of Fractional Order System of Duffing Equation with Quadratic and Cubic Nonlinearities. International Journal of Computer Sciences and Engineering, 07(05), 16-19.

BibTex Style Citation:
@article{Selvam_2019,
author = {A. George Maria Selvam, D. Vignesh, R. Janagaraj},
title = {Stability of Fractional Order System of Duffing Equation with Quadratic and Cubic Nonlinearities},
journal = {International Journal of Computer Sciences and Engineering},
issue_date = {3 2019},
volume = {07},
Issue = {05},
month = {3},
year = {2019},
issn = {2347-2693},
pages = {16-19},
url = {https://www.ijcseonline.org/full_spl_paper_view.php?paper_id=797},
doi = {https://doi.org/10.26438/ijcse/v7i5.1619}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v7i5.1619}
UR - https://www.ijcseonline.org/full_spl_paper_view.php?paper_id=797
TI - Stability of Fractional Order System of Duffing Equation with Quadratic and Cubic Nonlinearities
T2 - International Journal of Computer Sciences and Engineering
AU - A. George Maria Selvam, D. Vignesh, R. Janagaraj
PY - 2019
DA - 2019/03/10
PB - IJCSE, Indore, INDIA
SP - 16-19
IS - 05
VL - 07
SN - 2347-2693
ER -

           

Abstract

In physics, mechanics and engineering, Duffing equations are used in describing the oscillatory systems with non linearities and is famous in study of nonlinear dynamics. Here, we study the asymptotic stability of the fractional order unforced damped Duffing equation with quadratic nonlinearity. Local asymptotic stability conditions for commensurate order fractional derivative system with order lying in (0,2) is discussed without considering integer order. The stability of the system is investigated with fractional orders in two ranges (0,1) and (1,2). For different values of the parameters, examples with simulations are performed. Sensitivity of the system for the small variation in fractional order is analyzed with 2-Dimensional time plots. Lyapunov exponents for the system is investigated with plots and values of Lyapunov exponents are tabulated.

Key-Words / Index Term

Duffing equation, Fractional order system, Stability Nonlinear system

References

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