Aperiodic dynamics are known to be essential in the formation of perceptual mechanisms and representations in biological organisms. Advances in neuroscience and computational neurodynamics are helping us understand the properties of nonlinear systems that are fundamental in the selforganization of stable, complex patterns in many types of systems, from biological ecosystems to human economies and in biological brains. In this paper we introduce a neurological population model that is capable of replicating the important aperiodic dynamics observed in biological brains. We use the mechanism to self-organize cognitive maps in an autonomous agent.