  We construct a chaotic discrete-time continuous-state Hopfield network with
piecewise-affine nonnegative activation functions and weight matrix with small
positive entries. More precisely, there exists a Cantor set $C$ in the state
space such that the network has sensitive dependence on initial conditions at
initial states in $C$ and the network orbit of each initial state in $C$ has
$C$ as its $\omega$-limit set. The approach we use is based on tools developed
and employed recently in the study of the topological dynamics of
piecewise-contractions. The parameters of the chaotic network are explicitly
given.
