International Journal of Mathematics Trends and Technology
Volume 66 | Issue 4 | Year 2020 | Article Id. IJMTT-V66I4P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I4P507
In this work, we investigate the global stability of the following fourth- order rational difference equation xn+1 = (xbn-1xbn-2xn-3+xbn-1+xn-3+xbn-2+a)/(xbn-1xbn-2+xbn-1xn-3+xbn-2xn-3+1+a), (1) where a,bε[0,∞) and the initial values x-3,x-2,x-1,x0ε(0,∞).
[1] R.P.Agarwal, Difference Equations and InequalitiesSecond Ed. Dekker, New York, 1992, 2000. Qualitative properties for a fourth - order 7
[2] V.L.. Kocic, G. Ladas, Global behavior of nonliner difference equations of higher order with applications, Kluwer Academic, Dordrecht, 1993.
[3] M. R. S. Kulenovic, G. Ladas, L. F. Martins. I. W. Rodrignes, The dynamics of xn+1 = α+βx/A+Bxn+Cxn-1: Facts and conjectures, Comput. Math. Appl. 45(2003), 1087-1099.
[4] G. Ladas, Open problems and conjectures, J. Difference Equa. Appl. 2(1996), 449-452.
[5] X. Li, D. Zhu, Global asymptotic stability in a rational equationJ. Dif- ference. Equa. Appl. 9 (2003), 833-839.
[6] X. Li, D. Zhu, Global asymptotic stability for two recursive difference equations,Appl. Math. Comput. 150 (2004), 481-492.
[7] X. Li, D. Zhu, Global asymptotic stability of a nonlinear recursive se- quence,Appl. Math. Appl. 17 (2004), 833-838.
[8] X. Li, D. Zhu, Global asymptotic stability for a nonlinear delay difference equation,Appl. Math. J. Chinese Univ. Ser. B 17 (2002), 183-188.
[9] X. Li, Qualitative properties for a fourth-order rational difference equa- tion,Appl. Anal. Appl. 311 (2005) , 103-111.
[10] X. Li and R. P. Agarwal, The rule of trajectory structure and global asymptotic stability for a fourth-order rational difference equa- tion,J.Korean Math. Soc. 44 (2007), 787-797.
[11] X. Li, D. Zhu, Global asymptotic stability in a rational equation,J. Dif- ference. Equal. Appl. 9 (2003) 833-839.
[12] X. Li, D. Zhu, Global asymptotic stability for two recursive difference equation,Appl. Math. Comput. 150 (2004), 481-492.
[13] X. Li, D. Zhu, Global asymptotic stability of a nonlinear recursive se- quence,Appl. Math. Appl, 17 (2004), 833-838.
[14] X. Li, D. Zhu, Two rational recursive sequence,Comput. Math. Appl. 47 (2004), 1487-1494.
[15] X. Li, D. Zhu, Global asymptotic stability for a nonlinear delay difference equation.Appl. Math. J. Chinese Univ. Ser. B 17 (2002), 183-188.
[16] X. Li, D. Zhu, et al, A conjectures by G. Ladas,Appl. Math. J. Chinese Univ. Ser. B 13 (1998), 39-44. 8 Vu Van Khuong and Vu Nguyen Thanh
[17] X. Li, Boundedness and persistence and global asymptotic stability for a kind of delay difference equations with higher order,Appl. Math. Mech. (English) 23 (2003), 1331-1338.
[18] X. Li, G. Xiao, et al, Periodicity and strict oscillation for generalized Lyness equations,Appl. Math. Mech. (English) 21 (2000), 455-460.
[19] X. Li, Qualitative properties for a fourth-order rational difference equa- tions,J. Math. Anal. Appl. 311 (2005),103-111.
[20] X. Li, The rule of trajectory and global asymptotic stability for a fourth- order rational difference equation,J. Korean Math. Soc. 44 (2007), 787- 797.
[21] Vu Van Khuong and Mai Nam Phong on the global asymptotic stability of the difference equation xn+1 = (xn-1xn-3+x2n-1+a)/x2n-1xn-3+xn-1+a CIAA.
[22] Vu Van Khuong on the global asymptotically stable of the systems of two difference equations,JGRMA ISSN 2320-5822-Vol1. No4, (2013), April 2013.
[23] Vu Van Khuong, qualitative properties for a fourth-order rational differ- ence equation(II),Int. J. Math. Anal, Vol4, 2010, No13, 617-629. 14 (2010) No4, 597-606.
Vu Van Khuong, Vu Nguyen Thanh, "On the Global Asymptotic Stability of a Fourth-Order Rational Difference Equation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 4, pp. 44-51, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I4P507
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