Solutions and Periodicity of a Rational Recursive Sequences of Order Five

Abstract

In this paper, the solutions of the recursive sequences x n+1

Expression and behavior of the solutions of some rational recursive sequences

“…The long‐term behavior of the solutions of nonlinear difference equations of order greater than one has been extensively studied during the last decade. For example, various results about boundedness, stability, and periodic character of the solutions of the second‐order nonlinear difference equation, see .…”

Stability and Neimark–Sacker bifurcation of a ratio‐dependence predator–prey model

“…Yang and Li [10] studied the permanence of species for a delayed discrete ratio-dependent predator-prey model with monotonic functional response. Study of discrete dynamical behavior of systems is usually focussed on boundedness and persistence, existence and uniqueness of equilibria, periodicity, and there local and global stability (see for example, [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]), but there are few articles that discuss the dynamical behavior of discrete-time predator-prey models for exploring the possibility of bifurcation and chaos phenomena [26][27][28][29][30].…”

Investigating dynamical behaviors of the difference equation \(x_{n+1}= \frac{Cx_{n-5}}{A+Bx_{n-2}x_{n-5}}\)

“…Difference equations have potential applications in various fields of science such as game theory [2,3,5,6,17,18], mathematical biology [15,34], physics, and engineering [11]. Therefore, the study of the qualitative behavior of a nonlinear rational difference equations of higher orders [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] is of paramount importance because of its promising applications.…”