Fixed points and Stability of Damped and Unforced Duffing Equation, Solution and Graphs for Displacement and Velocity of that Equation using Matlab

Authors

  • Ajaya Kumar Singh  Department of Mathematics, Ekamra College, Bhubaneswar, Odisha, India

DOI:

https://doi.org//10.32628/IJSRST20715

Keywords:

Duffing Equation, Jacobi Elliptic Functions, Period, Boundedness

Abstract

The object of the present paper is to find the fixed points and their stability by matrix method of the duffing equation. The duffing equation can be expressed in and shown by MATLAB program and their graphs.

References

  1. A. K. Singh, Matlab Programming with Practical, Kalyani Publishers, Ludhiana, (2017).
  2. I. Kovacic and M. J. Brennan, The Duffing Equation: Non Linear Oscillators and their Behaviour, Willey, (2011).
  3. S. V. Wiggins, Application to the Dynamics of the Damped, Forced Duffing Oscillator. An Introduction to Applied Nonlinear Dynamical Systems and Chaos. Spring-Verlag, New York.
  4. J. S. Roy and S. Padhy, A Course on Ordinary and Partial Differential Equations (with Applications), Kalyani Publishers, Ludhiana, (2014).
  5. P. F. Bird and M. D. Friedman, Handbook of elliptic integrals for Engineers and Scientists, Springer, (1971).
  6. E. Ott, Chaos in Dynamical Systems, Cambridge University Press, New York, (1993).
  7. A. H. Salas and E. Jairo H. Castillo Applied Mathematical Sciences, 8(176), (2014).
  8. J. V. Armitage and W. F. Eberlein, Eliptic Functions, Cambridge University Press, (2006).
  9. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw – Hill, New York, (1978).
  10. D. Zwillinger, Handbook of Differential Equations, Academic Press, Boston, (1997).
  11. A. N. Nayfeth and D.T. Mook, Non-linear Oscillations, John Wiley, New York, (1973).

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Published

2020-01-30

Issue

Section

Research Articles

How to Cite

[1]
Ajaya Kumar Singh, " Fixed points and Stability of Damped and Unforced Duffing Equation, Solution and Graphs for Displacement and Velocity of that Equation using Matlab, International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011, Volume 7, Issue 1, pp.35-39, January-February-2020. Available at doi : https://doi.org/10.32628/IJSRST20715