  An effective self-consistent model is derived and used to study the dynamics
of an electron gas confined in a nonparabolic and anisotropic quantum well.
This approach is based on the equations of quantum hydrodynamics, which
incorporate quantum and nonlinear effects in an approximate fashion. The
effective model consists of a set of six coupled differential equations
(dynamical system) for the electric dipole and the size of the electron gas.
Using this model we show that: (i) High harmonic generation is related to the
appearance of chaos in the phase space, as attested by related Poincar\'e
sections; (ii) Higher order harmonics can be excited efficiently and with
relatively weak driving fields by making use of chirped electromagnetic waves.
