Abstract
We investigate some qualitative behavior of the solutions of the difference equation xn+ = ax n - bx n /(cx x - dxn-1), n = 0,1,..., where the initial conditions x-1, x0 are arbitrary real numbers and a, b, c, d are positive constants.
Highlights
In this paper we deal with some properties of the solutions of the difference equation xn+1 = axn − cxn bxn − dxn−1, n = 0, 1, . . . , (1.1)where the initial conditions x−1, x0 are arbitrary real numbers and a, b, c, d are positive constants.Recently, there has been a lot of interest in studying the global attractivity, boundedness character, and the periodic nature of nonlinear difference equations
We investigate some qualitative behavior of the solutions of the difference equation xn+1 = axn − bxn/(cxn − dxn−1), n = 0, 1, . . . , where the initial conditions x−1, x0 are arbitrary real numbers and a, b, c, d are positive constants
There has been a lot of interest in studying the global attractivity, boundedness character, and the periodic nature of nonlinear difference equations
Summary
In this paper we deal with some properties of the solutions of the difference equation xn+1. (i) The equilibrium point x of (1.2) is locally stable if for every > 0, there exists δ > 0 such that for all x−k, x−k+1, . (ii) The equilibrium point x of (1.2) is locally asymptotically stable if x is locally stable solution of (1.2) and there exists γ > 0 such that for all x−k, x−k+1, . Is a sufficient condition for the asymptotic stability of the difference equation yn+k + p1 yn+k−1 + · · · + pk yn = 0, n = 0, 1,. (a) If all roots of the polynomial equation (1.8) lie in the open unite disk |λ| < 1, the equilibrium x of (1.2) is asymptotically stable. (1.11) has a unique equilibrium x ∈ [a,b] and every solution of (1.11) converges to x
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