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Global Analysis of Solutions of a New Class of Rational Difference Equation
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
Department of Mathematics, The Faculty of Education, Al al-Bayt University, Mafraq, Jordan
- 1 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
- 2 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
- 3 Department of Mathematics, The Faculty of Education, Al al-Bayt University, Mafraq, Jordan
American Journal of Computational Mathematics·Volume 07 (2017)·Pages 495–503·Published 26 October 2017·DOI10.4236/ajcm.2017.74036
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Abstract
The study suggests asymptotic behavior of the solution to a new class of difference equations: . where a, b i , α and β are positive real numbers for i = 0, 1, · · · , k , and the initial conditions ψ -j , ψ -j+1 , · · · , ψ 0 are randomly positive real numbers where j = 2 k + 1 . Accordingly, we consider the stability, boundedness an d periodicity of the solutions of this recursive sequence. Indeed, we give some interesting counter examples in order to verify our strong results.
KeywordsDifference EquationStabilityBoundednessGlobale Stability and Periodicity
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