# Global behavior in rational difference equations

#### Abstract

We investigate the global behavior of the solutions of several rational difference equations. In particular, we study the global stability, the periodic nature, and the boundedness character of their solutions. We investigate three equations in this dissertation:^ In the first manuscript we study the equation xn+1=a+ gxn-1A+ Bxn+xn-2 ,n=0,1,&ldots; and establish that its solutions exhibit a trichotomy character which depends upon whether g is less than *A*, equal to *A*, or greater than *A*. ^ In the second manuscript, we investigate the equation xn+1=bxn +dxn-kA +xn-k,n= 0,1,&ldots; and present a detailed analysis of the global character of its solution. ^ In the third manuscript, we investigate the boundedness nature of all solutions of special cases of the equation xn+1=a+ bxn+g xn-1+dx n-2A+Bxn +Cxn-1 +Dxn-2,n =0,1,&ldots; We present many open problems and conjectures related to the boundedness of its solutions. ^ In all equations, the parameters are nonnegative real numbers and the initial conditions are arbitrary nonnegative real numbers such that the denominators are always positive. ^

#### Subject Area

Mathematics

#### Recommended Citation

Esha Chatterjee,
"Global behavior in rational difference equations"
(2005).
*Dissertations and Master's Theses (Campus Access).*
Paper AAI3186897.

http://digitalcommons.uri.edu/dissertations/AAI3186897