Periodicity and global attractivity of some difference equations
We investigate the periodic nature, the boundedness character, and the global attractivity of the positive solutions of three difference equations. ^ The first equation is a Lyness-type equation with periodic coefficients. Here we investigate the difference equations of the Lyness-type xn+1=anxn+b nxn-1,n=0 ,1,&ldots; and xn+1=max&cubl0;anxn ,bn&cubr0;xn-1, n=0,1,&ldots; where an= a0if nevena1 ifnodd and bn= b0ifn evenb1if nodd and a0,a1,b0,b1∈ &sqbl0;0,∞&parr0; , with a0+b0>0 and a1+b1>0 , and where the initial conditions x−1 and x0 are arbitrary positive real numbers. ^ The second equation which we study is the recursive sequence xn+1=maxAx pn,1xq n-1,n=0, 1,&ldots; ^ Here we investigate the boundedness character, the global stability, and the periodic behavior of the solutions of the above equation where A∈0,∞, p,q∈&sqbl0;0,∞&parr0; and the initial condition x−1 and x0 are arbitrary positive numbers. ^ Finally we investigate the global attractivity of the equilibrium solutions of the mosquito model xn+1=&parl0;axn+bxn-1e -xn-1&parr0;e-xn, n=0,1,&ldots; and the age structure population model yn+1=e-yn&parl0;a yn+byn-1&parr0;, n=0,1,&ldots;. ^
"Periodicity and global attractivity of some difference equations"
Dissertations and Master's Theses (Campus Access).