Recent "connectionist" models provide a new explanatory alternative to the digital computer as a model for brain function. Evidence from our EEG research on the olfactory bulb suggests that the brain may indeed use computational mechanisms like those found in connectionist models. In the present paper we discuss our data and develop a model to describe the neural dynamics responsible for odor recognition and discrimination. The results indicate the existence of sensory-and motor-specific information in the spatial dimension of EEG activity and call for new physiological metaphors and techniques of analysis. Special emphasis is placed in our model on chaotic neural activity. We hypothesize that chaotic behavior serves as the essential ground state for the neural perceptual apparatus, and we propose a mechanism for acquiring new forms of patterned activity corresponding to new learned odors. Finally, some of the implications of our neural model for behavioral theories are briefly discussed. Our research, in concert with the connectionist work, encourages a reevaluation of explanatory models that are based only on the digital computer metaphor.

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The main parts of the central olfactory system are the bulb (OB), anterior nucleus (AON), and prepyriform cortex (PC). Each part consists of a mass of excitatory or inhibitory neurons that is modelled in its noninteractive state by a 2nd order ordinary differential equation (ODE) having a static nonlinearity. The model is called a KOe or a KOi set respectively; it is evaluated in the "open loop" state under deep anesthesia. Interactions in waking states are represented by coupled KO sets, respectively KIe (mutual excitation) and KIi (mutual inhibition). The coupled KIe and KIi sets form a KII set, which suffices to represent the dynamics of the OB, AON, and PC separately. The coupling of these three structures by both excitatory and inhibitory feedback loops forms a KIII set. The solutions to this high-dimensional system of ODEs suffice to simulate the chaotic patterns of the EEG, including the normal low-level background activity, the high-level relatively coherent "bursts" of oscillation that accompany reception of input to the bulb, and a degenerate state of an epileptic seizure determined by a toroidal chaotic attractor. An example is given of the Ruelle-Takens-Newhouse route to chaos in the olfactory system. Due to the simplicity and generality of the elements of the model and their interconnections, the model can serve as the starting point for other neural systems that generate deterministic chaotic activity.

Humans are able to classify novel items correctly by category; some other animals have also been shown to do this. During category learning, humans group perceptual stimuli by abstracting qualities from similarity relationships of their physical properties. Forming categories is fundamental to cognition and can be independent of a 'memory store' of information about the items or a prototype. The neurophysiological mechanisms underlying the formation of categories are unknown. Using an animal model of category learning, in which frequency-modulated tones are distinguished into the categories of 'rising' and 'falling' modulation, we demonstrate here that the sorting of stimuli into these categories emerges as a sudden change in an animal's learning strategy. Electro-corticographical recording from the auditory cortex shows that the transition is accompanied by a change in the dynamics of cortical stimulus representation. We suggest that this dynamic change represents a mechanism underlying the recognition of the abstract quality (or qualities) that defines the categories.

Those classical models are reviewed that are most widely used by neurobiologists to explain the dynamics of neurons and neuron populations, and by modelers to implement artificial neural networks. Each neuron has input fibers called dendrites that integrate and an axon that transmits the output. The differing fiber architectures reflect these dissimilar dynamic operations. The basic tools to describe them are the RC model of the membrane, the core conductor model of the fibers, the Hodgkin–Huxley model of the trigger zone, and the modifiable synapse. Populations additionally require description of macroscopic state variables, the types of nonlinearity (most importantly the sigmoid curve and the dynamic range compression at the input to the cortex), and the types and strengths of connections. The properties of these neural masses can be characterized with the tools of nonlinear dynamics. These include description of point, limit cycle, and chaotic attractors for the cerebal cortex, as well as the types and mechanisms for the state transitions between basins of attraction during learning and perception.