  Continuous-time systems with switch-like behaviour occur in chemical
kinetics, gene regulatory networks and neural networks. Networks with hard
switching, as a limiting case of smooth sigmoidal switching, retain the richest
possible range of behaviors but are mathematically more tractable. The form of
an underlying discrete (fractional-linear) map encodes information on
existence, stability and exact periods of periodic orbits. In richly connected
structures with four or more variables, aperiodic behaviour can occur. We
investigate a simple 4-dimensional example with Boolean interaction terms in
which a Smale horseshoe-like object reveals chaotic dynamics.
