Global stability, two conjectures and Maple
For the differences equation \(u_{n+1}= f(u_{n-1}, u_n)\) with positive initial values the global aymptotic stability of the equilibrium is shown in the cases \(f(u,v)= (u+ pv)/(u+ qv)\) with \(0\leq q< p\), and \(f(u,v)= (p+ qv)/(1+ u)\) under more complicated conditions for \(p\), \(q\). Some generalizations are discussed, where a Maple program is used.
scientific article; zbMATH DE number 5127997