Stability Analysis of a Nonlinear Difference Equation

Affiliation(s)

Department of Mathematics, Faculty of Education, Erciyes University, Kayseri, Turkey.

Department of Mathematics, Faculty of Education, Erciyes University, Kayseri, Turkey.

ABSTRACT

The local and global behavior of the positive solutions of the difference equation

was investigated, where the parametersα,βandγand the initial conditions are arbitrary positive numbers. Furthermore, the characterization of the stability was studied with a basin that depends on the conditions of the coefficients. The analysis about the semi-cycle of positive solutions has end the study of this work.

Cite this paper

F. Bozkurt, "Stability Analysis of a Nonlinear Difference Equation,"*International Journal of Modern Nonlinear Theory and Application*, Vol. 2 No. 1, 2013, pp. 1-6. doi: 10.4236/ijmnta.2013.21001.

F. Bozkurt, "Stability Analysis of a Nonlinear Difference Equation,"

References

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[1] H. El-Metwally, E. A. Grove, G. Ladas, R. Levins and M. Radin, “On the Difference Equation x

[2] I. Ozturk, F. Bozkurt and S. Ozen, “On the Difference Equation,” Applied Mathematics and Computations, Vol. 181, No. 2, 2006, pp. 1387-1393. doi:10.1016/j.amc.2006.03.007

[3] I. Ozturk, F. Bozkurt and S. Ozen, “Global Asymptotic Behavior of the Difference Equation,” Applied Mathematic Letters, Vol. 22, No. 4, 2009, pp. 595-599. doi:10.1016/j.aml.2008.06.037

[4] C. H. Gibbons, M. R. S. Kulenovic, G. Ladas and H. D. Voulov, “On the Trichotomy Character of x

[5] M. M. El-Afifi and A. M. Ahmed, “On the Difference Equation,” Applied Mathematics and Computations, Vol. 144, No. 2-3, 2003, pp. 537-542. doi:10.1016/S0096-3003(02)00429-0

[6] W. S. He and W. T. Li, “Attractivity in a Nonlinear Delay Difference Equation,” Applied Mathematics E—Notes, Vol. 4, 2004, pp. 48-53.

[7] S. Ozen, I. Ozturk and F. Bozkurt, “On the Recursive Sequence,” Applied Mathematics and Computation, Vol. 188, No. 1, 2007, pp. 180-188. doi:10.1016/j.amc.2006.09.106

[8] K. Cunningham, et al., “On the Recursive Sequence,” Nonlinear Analysis, Vol. 47, No. 7, 2001, pp. 4603-4614. doi:10.1016/S0362-546X(01)00573-9

[9] C. Gibbons, M. R. S. Kulenovic and G. Ladas, “On the Recursive Sequence,” Mathematical Sciences Research Hot-Line, Vol. 4, No. 2, 2000, pp. 1-11.

[10] C. Celik, H. Merdan, O. Duman and O. Akin, “Allee Effects on Population Dynamics with Delay,” Chaos, Solitons and Fractals, Vol. 37, No. 1, 2008, pp. 65-74.