The global stability, boundedness, and periodicity character of certain difference equations
We study the global stability, the boundedness nature, and the periodic character of the positive solutions of the difference equation xn+1=a+bxn-1e-x n,n=0,1,&ldots; where the parameters α and β are positive real numbers and the initial conditions x−1 and x0 are arbitrary non-negative real numbers. ^ This problem was proposed by Dr. Richard Levins of the Harvard School of Public Health as a population model in Mathematical Biology. We consider α to be the immigration rate and β to be the population growth rate. ^ We will also investigate the periodic character and the boundedness nature of all positive solutions of following two max - type difference equations: xn+1=max 1xn,An xn-1, n=0,1,&ldots; and xn+1=max Anxn ,1xn-1 ,n=0,1,&ldots; where An∞ n=0 is a sequence of positive real numbers with prime period three and the initial conditions x−1 and x0 are arbitrary positive real numbers. ^
Michael Alexander Radin,
"The global stability, boundedness, and periodicity character of certain difference equations"
Dissertations and Master's Theses (Campus Access).