  We present a new chaotic system of three coupled ordinary differential
equations, limited to quadratic nonlinear terms. A wide variety of dynamical
regimes are reported. For some parameters, chaotic reversals of the amplitudes
are produced by crisis-induced intermittency, following a mechanism different
from what is generally observed in similar deterministic models. Despite its
simplicity, this system therefore generates a rich dynamics, able to model more
complex physical systems. In particular, a comparison with reversals of the
magnetic field of the Earth shows a surprisingly good agreement, and highlights
the relevance of deterministic chaos to describe geomagnetic field dynamics.
