Neuromodeling is usually motivated by a desire to better understand specific neural circuits, particularly those whose failure triggers human illnesses. Depression, anxiety, schizophrenia, Alzheimer's disease, memory impairment, paralysis, epilepsy, multiple sclerosis, Parkinson's disease, etc. are areas in which intense research efforts are being made so as to better understand and treat these conditions. In this respect, from a modeling perspective, one hypothesis is that the analysis of the connections between the neurons is fundamental. Apart from providing a better understanding of the conditions and symptoms of a disease, such an analysis also leads to a better understanding of the development and function of the normal brain. The brain is virtually unique in its exquisitely complex three dimensional structure. Although the structure and the functionality of other types of tissues can be explained without a precise knowledge of their shape and the specific connections of each cell, this is not easily achieved for the brain. The tools used today to analyze the shape and structure at the brain^Rs cellular level are scarcely capable of describing the precise performance of systems consisting of more than a handful of neurons. One must analyze the shape and connections of at least thousands, probably millions and perhaps billions of nerve cells before claiming to fully understand the structures that determine the behavior of flies, worms, mice, and humans. To the best of our knowledge, the problem of defining the minimum scale for modeling the brain (or large sections of the brain) remain unsolved.

In this context, research involving brain modeling has followed two distinct approaches, namely (a) those which involve a large scale network of neurons, and (b) those which incorporate a small scale network of neurons. Each of these models has advantages and disadvantages.

Objectives of our research:

1. We would like to demonstrate that if the brain is modeled as a large scale network of neurons, where each neuron has a fairly elementary model, the resulting network can demonstrate chaotic phenomena. In this regard, we intend to work with a primitive model of the pyramidal neuron of the piriform cortex.

2. We would like to demonstrate that if portions of the brain are modeled as small scale networks, the latter again demonstrates chaotic behavior. In this regard, we shall utilize the Hodgkin-Huxley neuron and a Bursting neuron to demonstrate that the chaos in the networks of such neurons can be controlled.