Global behavior of some nonlinear difference equations
We provide three results in this dissertation: first, we establish a method for determining the rate of convergence for third order, rational difference equations; second, we investigate the global behavior of a general, mth order equation; and last, we compare an autonomous, second order, rational difference equation to a nonautonomous counterpart. ^ Specifically, in the first manuscript we investigate the asymptotics of solutions of some special cases of the equation xn+1=a+bxn+g xn-1+dxn-2A+Bxn +Cxn-1+Dxn-2, n=0,1,&ldots; with positive parameters and nonnegative initial conditions. We give the precise results about the rate of convergence of the solutions by using Poincaré's and Perron's theorem. ^ In the second manuscript, we investigate the global character of solutions of the equation xn+1=bxn-l+dx n-kBxn-l+Dxn-k with positive parameters and nonnegative initial conditions. ^ In the third manuscript, we investigate the periodic nature, the boundedness character, the global asymptotic stability, and the rate of convergence of solutions of the difference equation xn+1=pn+xn-1 xn where the parameter pn is a period-two sequence with positive values and the initial conditions are positive. ^
Carol Boyd Overdeep,
"Global behavior of some nonlinear difference equations"
Dissertations and Master's Theses (Campus Access).