Explicit Solutions and Bifurcations for a System of Rational Difference Equations

Abstract

In this paper, we consider the explicit solution of the following system of nonlinear rational difference equations: x n + 1 = x n - 1 / x n - 1 + r , y n + 1 = x n - 1 y n / x n - 1 y n + r , with initial conditions x - 1 , x 0 and y 0 , which are arbitrary positive real numbers. By doing this, we encounter the hypergeometric function. We also investigate global dynamics of this system. The global dynamics of this system consists of two kind of bifurcations.

Asymptotic Behavior of Discrete Time Fuzzy Single Species Model

“…Difference equations or discrete time dynamical systems have many applications in economics, biology, computer science, control engineering, etc. (see, for example, [1][2][3][4][5][6][7][8][9][10] and the references therein). In the recent years, many researchers pay a close attention to the study on qualitative behavior of difference equation in mathematical biology and population dynamics [11][12][13].…”