This talk will focus on the dynamics of systems of neurons, and on the potential generality of non-classical, yet deterministic dynamics in the brain. To illustrate this, I will use three examples taken from very different animals and systems: olfactory circuits in insects, the camouflage system of cuttlefish and the cerebral cortex of reptiles. One of the goals of this juxtaposition is to emphasize the value of a comparative perspective in systems neuroscience: evolution helps us separate potentially general functional or computational principles from specific implementation details.