Global dynamics of some systems of higher-order rational difference equations

Abstract

In the present work, we study the qualitative behavior of two systems of higher-order rational difference equations. More precisely, we study the local asymptotic stability, instability, global asymptotic stability of equilibrium points and rate of convergence of positive solutions of these systems. Our results considerably extend and improve some recent results in the literature. Some numerical examples are given to verify our theoretical results. MSC: 39A10; 40A05

Global Dynamics of Higher-Order Exponential Systems of Difference Equations

“…where , , ( = 4, 5, ⋅ ⋅ ⋅ , 18) and , , ( = 0, −1) are positive real numbers. Khan and Qureshi [7] have explored the dynamical properties of the following exponential system of difference equations:…”

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:…”

Global Dynamics of Rational Difference Equations xn+1=xn+xLiu1, Peng2, Wang3 2017Discrete Dynamics in Nature and Society2040View full textAdd to dashboardCite

“…For other types of equations and systems, see [14][15][16][17][18][19][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. As for the definition of basin of attraction and the stable manifold and so on, see [35][36][37][38][39].…”