The position of a smooth ball resting on the inside surface of a hemispherical bowl is stable provided the bowl is concave upwards. However, the ball's position is unstable to small displacements if placed on the outer side of a hemispherical bowl when the bowl is concave downwards

In fluid flows, smooth laminar flows are stable to small disturbances only when certain conditions are satisfied. For example, in the flow of a homogeneous viscous fluid in a channel, the Reynolds number must be less than some critical value for the flow to be stable, and in a stratified shear flow, the Richardson number must be larger than a critical value for stability

When these conditions are not satisfied, infinitesimal disturbances may grow spontaneously and completely change the character of the original flow. Sometimes the disturbances can grow to finite amplitude and reach a new steady-state equilibrium. The new state may then become unstable to other types of disturbances, and may evolve to yet another steady state, and so on