On the Dynamics of the Nonlinear Rational Difference Equation x_{n+1}=Ax_{n}+Bx_{n-a}+((ax_{n-a}+bx_{n-k})/(cx_{n-a}+dx_{n-k}))

On the Dynamics of the Nonlinear Rational Difference Equation x_{n+1}=Ax_{n}+Bx_{n-a}+((ax_{n-a}+bx_{n-k})/(cx_{n-a}+dx_{n-k}))

H. S. Alshawee

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E. M. Elabbasy

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Mansoura University

$On the Dynamics of the Nonlinear Rational Difference Equation x_{n+1}=Ax_{n}+Bx_{n-a}+((ax_{n-a}+bx_{n-k})/(cx_{n-a}+dx_{n-k}))$

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Abstract

Both the optimization and equilibrium principles turn out to be more akin to common sense than to science. They have been postulated as describing markets, but lack the required empirical underpinning. Optimization is not a magic cure. In order to particularly circumvent some of the technical obstacles for a control problem , it turns out to be practically effective to reduce the system dynamics to a system of ordinary differential equations of considerably higher dimension, Such an approach might replace a theoretical difficulty by a greatly increased computational problem.

References

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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No ethics committee approval was required for this article type.

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How to Cite This Article

H. S. Alshawee. 2015. \u201cOn the Dynamics of the Nonlinear Rational Difference Equation x_{n+1}=Ax_{n}+Bx_{n-a}+((ax_{n-a}+bx_{n-k})/(cx_{n-a}+dx_{n-k}))\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 15 (GJSFR Volume 15 Issue F9): .

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GJSFR Volume 15 Issue F9
Pg. 33- 43

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

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Classification

GJSFR-F Classification: MSC 2010: 39A10, 39A11

Submission ReceivedNovember 1, 2015
Peer Review Double Blind
Handling Editor
Accepted November 29, 2015
Published December 14, 2015

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v1.2

Issue date

December 12, 2015

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Article Matrices

Total Score: 102

Country: Egypt

Subject: Global Journal of Science Frontier Research - F: Mathematics & Decision

Authors: E. M. Elabbasy, H. S. Alshawee (PhD/Dr. count: 0)

View Count (all-time): 151

Total Views (Real + Logic): 3882

Total Downloads (simulated): 1973

Publish Date: 2015 12, Sat

Monthly Totals (Real + Logic):

Month 1: 34 views
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Total Views: 3882

Total Downloads: 1973

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