Study of the asymptotic behavior of the solutions of three systems of difference equations of exponential form

In this paper we study the boundedness, the persistence and the asymptotic behavior of the positive solutions of the following systems of two difference equations of exponential form: xnþ1 ¼ a þ be � yn c þ yn� 1 ; y nþ1 ¼ d þ � e � xn f þ xn� 1 ;

[1]  Claude Froeschlé,et al.  Analysis and modelling of discrete dynamical systems , 1998 .

[2]  Stevo Stevi´c,et al.  ON THE RECURSIVE SEQUENCE $x_{n+1}=x_{n-1}/g(x_n)$ , 2002 .

[3]  Stevo Stević,et al.  On the Behaviour of the Solutions of a Second-Order Difference Equation , 2007 .

[4]  G. Ladas,et al.  On the Recursive Sequencexn + 1 = α + xn − 1/xn☆ , 1999 .

[5]  Lothar Berg,et al.  On the Asymptotics of Nonlinear Difference Equations , 2002 .

[6]  Wanbiao Ma,et al.  A Necessary and Sufficient Condition for Permanence of a Lotka–Volterra Discrete System with Delays , 2001 .

[7]  Leah Edelstein-Keshet,et al.  Mathematical models in biology , 2005, Classics in applied mathematics.

[8]  Stevo Stevic,et al.  Eventually constant solutions of a rational difference equation , 2009, Appl. Math. Comput..

[9]  S. Stević.  Nontrivial solutions of a higher-order rational difference equation , 2008 .

[10]  Lothar Berg,et al.  Inclusion Theorems for Non-linear Difference Equations with Applications , 2004 .

[11]  M. A. El-Moneam,et al.  Dynamics of the Rational Difference Equation , 2014 .

[12]  Стево Стевич,et al.  Нетривиальные решения рациональных разностных уравнений высших порядков@@@Nontrivial Solutions of a Higher-Order Rational Difference Equation , 2008 .

[13]  R. Levins,et al.  On the difference equation xn+1=α+βxn−1e−xn , 2001 .

[14]  Periodically forced nonlinear systems of difference equations , 1998 .

[15]  S. Stević.  On monotone solutions of some classes of difference equations , 2006 .

[16]  Rational systems in the plane , 2009 .

[17]  C. Schinas,et al.  On the nonautonomous difference equation , 2011 .

[18]  C. J. Schinas,et al.  On the nonautonomous difference equation xn+1 = An + (xpn-1 / xqn) , 2011, Appl. Math. Comput..

[19]  Ravi P. Agarwal,et al.  Difference equations and inequalities , 1992 .

[20]  Stevo Stević,et al.  Global stability and asymptotics of some classes of rational difference equations , 2006 .

[21]  Garyfalos Papaschinopoulos,et al.  On a modification of a discrete epidemic model , 2010, Comput. Math. Appl..

[22]  Ke Chen,et al.  Applied Mathematics and Computation , 2022 .

[23]  Stevo Stevic,et al.  On the recursive sequence xn+1 = max{c, xpn/xpn-1} , 2008, Appl. Math. Lett..

[24]  On the Difference Equation xn+1=xnxn-2-1 , 2011 .

[25]  E. Camouzis,et al.  Open Problems and Conjectures , 2008 .

[26]  S. Stević.  Asymptotic behavior of solutions of a nonlinear difference equation with continuous argument , 2004 .

[27]  S. Elaydi.  An introduction to difference equations , 1995 .

[28]  E. Camouzis,et al.  On the Dynamics of a Rational Difference Equation, Part 1 , 2008 .

[29]  V. Kocić,et al.  Global Behavior of Nonlinear Difference Equations of Higher Order with Applications , 1993 .

[30]  C. Kent.  Convergence of solutions in a nonhyperbolic case , 2001 .

[31]  Mustafa R. S. Kulenovic,et al.  A coupled system of rational difference equations , 2002 .

[32]  Stevo Stević,et al.  On the Recursive Sequence xn=1 , 2007 .

[33]  James F. Selgrade,et al.  Global asymptotic behavior of a two-dimensional difference equation modelling competition , 2003 .

[34]  B. Shi,et al.  Oscillation and global asymptotic stability in a discrete epidemic model , 2003 .

[35]  I. Ozturk,et al.  On the difference equation yn+1=(alpha + beta e-yn) / (gamma + yn-1) , 2006, Appl. Math. Comput..

[36]  Stevo Stević,et al.  Asymptotics of Some Classes of Higher-Order Difference Equations , 2007 .

[37]  J. Lawton,et al.  Dynamic complexity in predator-prey models framed in difference equations , 1975, Nature.

[38]  Stevo Stevic,et al.  On a class of third-order nonlinear difference equations , 2009, Appl. Math. Comput..

[39]  On the global character of solutions of the system: , 2012 .

[40]  Lothar Berg,et al.  On the asymptotics of the difference equation , 2008 .

[41]  Stevo Stevic.  On a system of difference equations , 2011, Appl. Math. Comput..

[42]  Stevo Stević,et al.  On a nonlinear generalized max-type difference equation , 2011 .

[43]  Stevo Stevic,et al.  Existence of nontrivial solutions of a rational difference equation , 2007, Appl. Math. Lett..

[44]  Stevo Stević,et al.  Asymptotic behavior of a sequence defined by iteration with applications , 2002 .

[45]  Alaa E. Hamza,et al.  On the recursive sequence x n+1 =.... , 2008 .

[46]  S. Stević.  On a Discrete Epidemic Model , 2007 .

[47]  Stevo Stevic,et al.  On positive solutions of a (k+1)th order difference equation , 2006, Appl. Math. Lett..