Stability analysis of a discrete biological model

Abstract

In this paper, we investigate the equilibrium point, local and global behavior of the unique positive equilibrium point, and rate of convergence of positive solutions of following discrete biological model: [Formula: see text] where parameters [Formula: see text] and the initial conditions [Formula: see text] are positive real numbers. Some numerical examples are given to verify theoretical results.

Global dynamics of a 3×6 exponential system of difference equations

“…Now, we will study the rate of convergence of positive solution of system (3), following the method. [8][9][10][11][12] Theorem 6. If {(x n , y n , z n )} be a positive solution of (3) such that…”

Global dynamics of (1,2)- type systems of difference equations

“…This made the study of qualitative behavior of difference equations an active area of research (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and references cited therein). For instance, Touafek and Elsayed [18,19] investigated the behavior of following systems of difference equations:…”

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].…”