International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2557

Full Length Research Paper

Solution and dynamics of a fourth rational difference equation

E. M. Elsayed
Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, 
Email: [email protected], [email protected]

  •  Accepted: 27 August 2012
  •  Published: 01 October 2013


In this paper, we get the form of the solutions of the following nonlinear recursive sequences of order four  where the initial conditionsare arbitrary real numbers. Also, we study some qualitative behaviors of the solutions as periodicity character of the solutions of these different equations and we obtain the equlibrium points of considered difference equations in order to investigate the local stability of these equlibrium points by using the linearized equation. We presented some numerical examples by giving some numerical values for the initial values and the coefficients of each case. Some figures have been given to explain the behavior of the obtained solutions in the case of numerical examples by using the mathematical program Matlab to confirm the obtained results.


Key words: Difference equations, recursive sequences, stability, periodic solution, Mathematics subject classification: 39A10.

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