Abstract
This article is concerned with the following rational difference equation y n+1= (y n + y n-1)/(p + y n y n-1) with the initial conditions; y -1, y 0 are arbitrary positive real numbers, and p is positive constant. Locally asymptotical stability and global attractivity of the equilibrium point of the equation are investigated, and non-negative solution with prime period two cannot be found. Moreover, simulation is shown to support the results.
Highlights
Difference equations are applied in the field of biology, engineer, physics, and so on [1]
The study of properties of rational difference equations has been an area of intense interest in the recent years [6,7]
There has been a lot of work deal with the qualitative behavior of rational difference equation
Summary
Difference equations are applied in the field of biology, engineer, physics, and so on [1]. (1) The equilibrium point xof Equation 2 is locally stable if for every ε > 0, there exists δ > 0, such that for any initial data x-k, x-k+1, ..., x0 Î I, with (2) The equilibrium point xof Equation 2 is locally asymptotically stable if xis locally stable solution of Equation 2, and there exists g > 0, such that for all x-k, x-k+1, ..., x0 Î I, with
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