Global asymptotic stability in quadratic systems

A classical problem in the qualitative theory of differential systems that is relevant for its applications, is to characterize the differential systems which are globally asymptotically stable, that is differential systems having a unique equilibrium point for which all their orbits, with the exception of the equilibrium point, tend in forward time to this equilibrium point.Here we provide three conditions that characterize the global asymptotic stability for planar quadratic polynomial differential systems. Using these three conditions we characterize all planar quadratic polynomial differential systems that are globally asymptotically stable. For more information see https://ejde.math.txstate.edu/Volumes/2025/36/abstr.html