Global dynamics of a higher order difference equation with a quadratic term

Abstract

In this paper, we investigate the dynamics of following higher order di¤erence equation x n+1 = A + B x n x 2 n m with A; B and initial conditions are positive numbers, and m 2 f2; 3; g. Especially we study the boundedness, periodicity, semi-cycles, global asymptotically stability and rate of convergence of solutions of related higher order di¤erence equations.

Dynamics of a Higher-Order Three-Dimensional Nonlinear System of Difference Equations

“…Finally, they showed that the positive solutions of System (3) are boundedness and persistence, and that the unique positive equilibrium point of System (2) is globally asymptotically stable. Other related difference equations and systems of difference equations can be found in references [10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Bazi Fark Denklemleri̇ni̇n Ayarlanmiş Jacobsthal-Padovan Sayilari İle İli̇şki̇li̇ Tam Çözümleri̇

“…Recently there has been a rapid increase in studying the theory and applications of difference equations, for related studies, see [3,4,5,19,20]. Especially, the studies that concern the relation between the special sequences and the closed form of the solutions of difference equations or systems have been received great interest by many researchers for a long time.…”

Dynamics of a System of Higher Order Difference Equations with Quadratic Terms

“…In [11], Taşdemir studied the periodicity, boundedness, semi-cycles, global asymptotically stability and rate of convergence of solutions of the following higher order difference equation…”