ABSTRACT
In this monograph, we present the known results and derive several new ones on the boundedness, the global stability, and the periodicity of solutions of all rational difference equations of the form
xn+1 = α+ βxn + γxn−1 A+Bxn + Cxn−1
, n = 0, 1, . . . (1)
where the parameters α, β, γ, A,B,C are nonnegative real numbers and the initial conditions x−1 and x0 are arbitrary nonnegative real numbers such that
A+Bxn + Cxn−1 > 0 for all n ≥ 0. We believe that the results about Eq(1) are of paramount importance in their own
right and furthermore we believe that these results offer prototypes towards the development of the basic theory of the global behavior of solutions of nonlinear difference equations of order greater than one. The techniques and results which we develop in this monograph to understand the dynamics of Eq(1) are also extremely useful in analyzing the equations in the mathematical models of various biological systems and other applications.
