Abstract: One characteristic of nonlinear dynamical systems is that they can have more than one stable equilibrium. Perturbations of the variables or changes in the parameters can cause the system to abruptly switch from one equilibrium to the other from which it is hard to recover (what Al Gore calls a "tipping point"). Furthermore, equilibria can become unstable and give birth to periodic oscillations and even chaos. Hence, in addition to static attractors, there can be limit cycles and strange attractors, and several such attractors can coexist in even simple systems. Sometimes these attractors are "hidden" in the sense that they cannot be found by starting from the vicinity of an unstable equilibrium. Such hidden attractors can be catastrophic if the system is a building, a bridge, or an airplane wing. Examples of such behavior will be illustrated in very simple systems of differential equations and with simple demonstrations.