Stability of a generalized Putnam equation
The authors prove that the equilibrium solution \(\bar{x}=1\) of the difference equation, \[ x_{n+1}=\frac{x_n+x_{n-1}+Ax_{n-2}x_{n-3}}{Ax_n x_{n-1} + x_{n-2} +x_{n-3}},\quad n=0,~1,~2,\dots \] with positive initial conditions is globally asymptotically stable if \(1\leq A<2\). They also conjecture that the equilibrium solution \(\bar{x}=1\) is globally asymptotically stable if \(A<\alpha\) where \(\alpha\approx 3.424.\)
scientific article; zbMATH DE number 5563167
scientific article