×

zbMATH — the first resource for mathematics

On the solutions of the system of difference equations \(x_{n+1}=\max\{A/x_n,y_n/x_n\}\), \(y_{n+1}=\max\{A/y_n,x_n/y_n\}\). (English) Zbl 1178.39013
Summary: We study the behavior of the solutions of the following system of difference equations
\[ x_{n+1}=\max\{A/x_n,y_n/x_n\},\quad y_{n+1}=\max\{A/y_n,x_n/y_n\} \] where the constant \(A\) and the initial conditions are positive real numbers.

MSC:
39A20 Multiplicative and other generalized difference equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] A. M. Amleh, Boundedness periodicity and stability of some difference equations, Ph.D. thesis, University of Rhode Island, Kingston, Rhode Island, USA, 1998.
[2] C. \cCinar, S. Stević, and \DI. Yal, “On positive solutions of a reciprocal difference equation with minimum,” Journal of Applied Mathematics & Computing, vol. 17, no. 1-2, pp. 307-314, 2005. · Zbl 1074.39002
[3] S. N. Elaydi, An Introduction to Difference Equations, Undergraduate Texts in Mathematics, Springer, New York, NY, USA, 1996. · Zbl 0840.39002
[4] J. Feuer, “Periodic solutions of the Lyness max equation,” Journal of Mathematical Analysis and Applications, vol. 288, no. 1, pp. 147-160, 2003. · Zbl 1042.39002
[5] A. Geli\csken, C. \cCinar, and R. Karata\cs, “A note on the periodicity of the Lyness max equation,” Advances in Difference Equations, vol. 2008, Article ID 651747, 5 pages, 2008. · Zbl 1149.39004
[6] A. Geli\csken, C. \cCinar, and \DI. Yal, “On the periodicity of a difference equation with maximum,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 820629, 11 pages, 2008. · Zbl 1149.39005
[7] E. Janowski, V. L. Kocic, G. Ladas, and G. Tzanetopoulos, “Global behavior of solutions of xn+1=[max{xnk,A}]/xn - 1,” Journal of Difference Equations and Applications, vol. 3, no. 3-4, pp. 297-310, 1998. · Zbl 0895.39004
[8] M. R. S. Kulenević and G. Ladas, Dynamics of Second Order Rational Difference Equations with Open Problems and Conjecture, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2002. · Zbl 0981.39011
[9] D. P. Mishev, W. T. Patula, and H. D. Voulov, “A reciprocal difference equation with maximum,” Computers & Mathematics with Applications, vol. 43, no. 8-9, pp. 1021-1026, 2002. · Zbl 1050.39015
[10] L. A. Moybé and A. S. Kapadia, Difference Equations with Public Health Applications, CRC Press, New York, NY, USA, 2000.
[11] G. Papaschinopoulos and V. Hatzifilippidis, “On a max difference equation,” Journal of Mathematical Analysis andApplications, vol. 258, no. 1, pp. 258-268, 2001. · Zbl 0986.39005
[12] G. Papaschinopoulos, J. Schinas, and V. Hatzifilippidis, “Global behavior of the solutions of a max-equation and of a system of two max-equations,” Journal of Computational Analysis and Applications, vol. 5, no. 2, pp. 237-254, 2003. · Zbl 1034.39008
[13] W. T. Patula and H. D. Voulov, “On a max type recurrence relation with periodic coefficients,” Journal of Difference Equations and Applications, vol. 10, no. 3, pp. 329-338, 2004. · Zbl 1050.39017
[14] G. Stefanidou and G. Papaschinopoulos, “The periodic nature of the positive solutions of a nonlinear fuzzy max-difference equation,” Information Sciences, vol. 176, no. 24, pp. 3694-3710, 2006. · Zbl 1122.39008
[15] S. Stević, “On the recursive sequence xn+1=max{c,xnp/xn - 1p},” Applied Mathematics Letters, vol. 21, no. 8, pp. 791-796, 2008. · Zbl 1152.39012
[16] D. \cSimsek, C. \cCinar, and \DI. Yal, “On the solutions of the difference equation xn+1=max{1/xn - 1,xn - 1},” International Journal of Contemporary Mathematical Sciences, vol. 1, no. 9-12, pp. 481-487, 2006.
[17] D. \cSimsek, B. Demir, and A. S. Kurbanlı, “xn+1=max{1/xn,yn/xn},yn+1=max{1/yn,xn/yn},” Denklem Sistemlerinin Üzerine. In press.
[18] C. T. Teixeria, Existence stability boundedness and periodicity of some difference equations, Ph.D. thesis, University of Rhode Island, Kingston, Rhode Island, USA, 2000.
[19] S. Valicenti, Periodicity and global attractivity of some difference equations, Ph.D. thesis, University of Rhode Island, Kingston, Rhode Island, USA, 1999.
[20] H. D. Voulov, “On the periodic character of some difference equations,” Journal of Difference Equations and Applications, vol. 8, no. 9, pp. 799-810, 2002. · Zbl 1032.39004
[21] H. D. Voulov, “Periodic solutions to a difference equation with maximum,” Proceedings of the American Mathematical Society, vol. 131, no. 7, pp. 2155-2160, 2003. · Zbl 1019.39005
[22] \DI. Yal, B. D. Iri\vcanin, and C. \cCinar, “On a max-type difference equation,” Discrete Dynamics in Nature and Society, vol. 2007, Article ID 47264, 10 pages, 2007. · Zbl 1152.39016
[23] \DI. Yal, C. \cCinar, and M. Atalay, “On the solutions of systems of difference equations,” Advances in Difference Equations, vol. 2008, Article ID 143943, 9 pages, 2008. · Zbl 1146.39023
[24] X. Yan, X. Liao, and C. Li, “On a difference equation with maximum,” Applied Mathematics and Computation, vol. 181, pp. 1-5, 2006. · Zbl 1148.39303
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.