For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain li...For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain limiting equation.展开更多
This paper is concerned with a host-macroparasite difference model. By applying the con- traction mapping fixed point theorem, we prove the existence of unique almost periodic positive solution. Moreover, we investiga...This paper is concerned with a host-macroparasite difference model. By applying the con- traction mapping fixed point theorem, we prove the existence of unique almost periodic positive solution. Moreover, we investigate the exponential stability of Mmost periodic solution by means of Lyapunov functional.展开更多
In this paper, we investigate some qualitative behavior of the solutions of the difference equation where the coefficients a, b and c<sub>i</sub> are positive real numbers, and where the initial conditions...In this paper, we investigate some qualitative behavior of the solutions of the difference equation where the coefficients a, b and c<sub>i</sub> are positive real numbers, and where the initial conditions are arbitrary positive real numbers.展开更多
The main purpose of this paper is to study the dynamic behavior of the rational difference equation of the fourth order Where α, β and γ are positive constants and the initial conditions y<sub>-3</sub>,...The main purpose of this paper is to study the dynamic behavior of the rational difference equation of the fourth order Where α, β and γ are positive constants and the initial conditions y<sub>-3</sub>, y<sub>-2</sub>, y<sub>-1</sub>, y<sub>0</sub> are arbitrary positive real numbers. Also, we obtain the solution of some special cases of this equation and investigate the existence of a periodic solutions of these equations. Finally, some numerical examples will be given to explicate our results. .展开更多
Difference equations or discrete dynamical systems is diverse field whose impact almost every branch of pure and ap- plied mathematics. Every dynamical system an+1=f(an) determines a difference equation and vise versa...Difference equations or discrete dynamical systems is diverse field whose impact almost every branch of pure and ap- plied mathematics. Every dynamical system an+1=f(an) determines a difference equation and vise versa. We ob-tain in this paper the solution and periodicity of the following difference equation. xn+1=(xnxn-2xn-4)/(xn-1xn-3xn-5, (1) n=0,1,... where the initial conditions x-5,x-4,x-3,x-2,x-1 and x0 are arbitrary real numbers with x-1,x-3 and x-5 not equal to be zero. On the other hand, we will study the local stability of the solutions of Equation (1). Moreover, we give graphically the behavior of some numerical examples for this difference equation with some initial conditions.展开更多
This paper is concerned with asymptotic behavior of the solution of a new class of rational Difference Equations. We consider the local and global stability of the solution. Moreover we investigate the new periodic ch...This paper is concerned with asymptotic behavior of the solution of a new class of rational Difference Equations. We consider the local and global stability of the solution. Moreover we investigate the new periodic character (periodic two) of solutions of these equations. Finally, we give some interesting counter examples in order to verify our strong results.展开更多
The study suggests asymptotic behavior of the solution to a new class of difference equations: . where a, bi, α and β are positive real numbers for i = 0, 1, · · · , k , and the initial conditions ψ-...The study suggests asymptotic behavior of the solution to a new class of difference equations: . where a, bi, α and β are positive real numbers for i = 0, 1, · · · , k , and the initial conditions ψ-j, ψ-j+1, · · ·, ψ0 are randomly positive real numbers where j = 2k + 1. Accordingly, we consider the stability, boundedness and periodicity of the solutions of this recursive sequence. Indeed, we give some interesting counter examples in order to verify our strong results.展开更多
文摘For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain limiting equation.
基金The author thanks the referees for their valuable comments and suggestions in improving the presentation of the manuscript. This work is supported by Natural Science Foundation of Education Department of Anhui Province （KJ2014A043）.
文摘This paper is concerned with a host-macroparasite difference model. By applying the con- traction mapping fixed point theorem, we prove the existence of unique almost periodic positive solution. Moreover, we investigate the exponential stability of Mmost periodic solution by means of Lyapunov functional.
文摘In this paper, we investigate some qualitative behavior of the solutions of the difference equation where the coefficients a, b and c<sub>i</sub> are positive real numbers, and where the initial conditions are arbitrary positive real numbers.
文摘The main purpose of this paper is to study the dynamic behavior of the rational difference equation of the fourth order Where α, β and γ are positive constants and the initial conditions y<sub>-3</sub>, y<sub>-2</sub>, y<sub>-1</sub>, y<sub>0</sub> are arbitrary positive real numbers. Also, we obtain the solution of some special cases of this equation and investigate the existence of a periodic solutions of these equations. Finally, some numerical examples will be given to explicate our results. .
文摘Difference equations or discrete dynamical systems is diverse field whose impact almost every branch of pure and ap- plied mathematics. Every dynamical system an+1=f(an) determines a difference equation and vise versa. We ob-tain in this paper the solution and periodicity of the following difference equation. xn+1=(xnxn-2xn-4)/(xn-1xn-3xn-5, (1) n=0,1,... where the initial conditions x-5,x-4,x-3,x-2,x-1 and x0 are arbitrary real numbers with x-1,x-3 and x-5 not equal to be zero. On the other hand, we will study the local stability of the solutions of Equation (1). Moreover, we give graphically the behavior of some numerical examples for this difference equation with some initial conditions.
文摘This paper is concerned with asymptotic behavior of the solution of a new class of rational Difference Equations. We consider the local and global stability of the solution. Moreover we investigate the new periodic character (periodic two) of solutions of these equations. Finally, we give some interesting counter examples in order to verify our strong results.
文摘The study suggests asymptotic behavior of the solution to a new class of difference equations: . where a, bi, α and β are positive real numbers for i = 0, 1, · · · , k , and the initial conditions ψ-j, ψ-j+1, · · ·, ψ0 are randomly positive real numbers where j = 2k + 1. Accordingly, we consider the stability, boundedness and periodicity of the solutions of this recursive sequence. Indeed, we give some interesting counter examples in order to verify our strong results.
