An equilibrium solution y = c is called asymptotically stable (or attracting) if all nearby solutions converge to c. More precisely, there is an interval (a, b) containing c, such that for every c0 in (a, b), the solution y = f(x) to the initial-value problem y(0) = c0 has limx!1 f(x) = c Remark: Think about this like a ball at the bottom of a valley. If we push it a little, it will still return to the bottom after rocking back and forth