In the fields of artificial neural networks and robotics, complicated, often high-dimensional systems can be designed using evolutionary/other algorithms to successfully solve very complex tasks. However, dynamical analysis of the underlying controller can often be near impossible, due to the high dimension and nonlinearities in the system. In this paper, we propose a more restricted form of controller, such that the underlying dynamical systems are forced to contain a dynamical object called a heteroclinic network. Systems containing heteroclinic networks share some properties with finite-state machines (FSMs) but are not discrete: both space and time are still described with continuous variables. Thus, we suggest that the heteroclinic networks can provide a hybrid between continuous and discrete systems. We investigate this innovated architecture in a minimal categorical perception task. The similarity of the controller to an FSM allows us to describe some of the system's behaviors as transition between states. However, other, essential behavior involves subtle ongoing interaction between the controller and the environment that eludes description at this level.