Global attractivity and stability in some monotone discrete dynamical systems

The existence of globally attractive order intervals for some strongly monotone discrete dynamical systems in ordered Banach spaces is first proved under some appropriate conditions. With the strict sublinearity assumption, threshold results on global asymptotic stability are then obtained. As applications, the global asymptotic behaviours of nonnegative solutions for time-periodic parabolic equations and cooperative systems of ordinary differential equations are discussed and some biological interpretations and concrete application examples are also given.