Existence, stability, boundedness, and periodicity of some difference equations
We investigate the asymptotic behavior, the oscillatory character and the periodic nature of solutions of the difference equation xn+1=maxxn ,Axnxn-1 ,n=0,1,&ldots; where A is a real parameter and the initial conditions are arbitrary nonzero real numbers. ^ We also give a detailed description of the set of initial conditions x0,y0 ∈R2 for which the system of difference equations with real parameters a, b, c, and d xn+1=axn +byn yn+1=cxn+ dyn ,n=0,1,&ldots; is well defined for all n ≥ 0. We then present an analysis of the short term and long term behavior of its solutions. ^ Finally we investigate the periodic character and the global stability of solutions of yn+1=p+yn-1qy n+yn-1,n=0,1,&ldots; with positive parameters and positive initial conditions. ^
Christopher Todd Teixeira,
"Existence, stability, boundedness, and periodicity of some difference equations"
Dissertations and Master's Theses (Campus Access).