Abstract
In this article we study the difference equation where the initial conditions x -r , x -r+1, x -r+2,..., x 0 are arbitrary positive real numbers, r = max{l, k, p, q} is nonnegative integer and a, b, c are positive constants: Also, we study some special cases of this equation.
Highlights
The purpose of this article is to investigate the global attractivity of the equilibrium point, and the asymptotic behavior of the solutions of the following difference equation xn+1 (1)where the initial conditions x-r, x-r+1, x-r+2,..., x0 are arbitrary positive real numbers, r = max{l, k, p, q} is nonnegative integer and a, b, c are positive constants: we obtain the form of the solution of some special cases of Equation 1 and some numerical simulations to the equation are given to illustrate our results.Let us introduce some basic definitions and some theorems that we need in the sequel.Let I be some interval of real numbers and let f : Ik+1 → I, be a continuously differentiable function
Where the initial conditions x-r, x-r+1, x-r+2,..., x0 are arbitrary positive real numbers, r = max{l, k, p, q} is nonnegative integer and a, b, c are positive constants: we study some special cases of this equation
1 Introduction The purpose of this article is to investigate the global attractivity of the equilibrium point, and the asymptotic behavior of the solutions of the following difference equation xn+1
Summary
1 Introduction The purpose of this article is to investigate the global attractivity of the equilibrium point, and the asymptotic behavior of the solutions of the following difference equation xn+1 Axn−l xn−k bxn−p − cxn−q where the initial conditions x-r, x-r+1, x-r+2,..., x0 are arbitrary positive real numbers, r = max{l, k, p, q} is nonnegative integer and a, b, c are positive constants: we obtain the form of the solution of some special cases of Equation 1 and some numerical simulations to the equation are given to illustrate our results.
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