Signals generated in a recurrently connected network of sigmoidal modes may be stable, periodic or chaotic. This paper shows that the behaviour of such a network may be controlled by adjusting the magnitude of a global parameter s that determines the sigmoid steepness. For three nodes, the transition to chaos is shown to be consistent with Feigenbaum’s model of critical nonliner systems. Large systems whose connection weights and biases evolve by a modified Hebbian rule are also shown to become stable or chaotic, depending on the magnitude of s. In the final part of the paper a recurrent network that received input from sensors is used to generate output that drives the motion of a simulated machine. It is shown that the machine motion is strongly influenced by an emitting source, such as a light, which activates the network sensors. The machine may be strongly but erratically attracted to the source, or it may be repelled, depending on the sign of the connection weights between the sensors and the network.