Explaining the processing of information in the brain at its most simple level (the firing and transmission of electrical signals) is of immense importance to science. However due to the complexity and size of the brain, scientists often focus on smaller regions. Understanding the methods by which the synchronized firing of small clusters of neurons can create complex phenomena such as working memory, discriminatory selection and other commonly seen functions of the brain forms the basis for understanding advanced processes in the brain. Neuronal cultures show remarkable properties of self-organization and synchronization when allowed to grow without interference. Clusters of neurons are seen to form without any external help in these neuronal cultures. These clusters proceed to form a network of interconnects which allows the synchronized firing of action potentials. This synchronization is at two levels, synchronized bursting events (SBEs) of action potentials within each cluster, as well as the synchronization of these SBEs that occur in connected clusters.
A computational model of the electrical oscillations in neuronal network representing a single cluster of neurons, as well as two connected clusters is provided in this thesis. This model allows us to examine the different factors that cause synchronization as well to show the extent of information processing that is possible in a randomly generated network of clusters.
The model generated shows that the delay between clusters plays a critical role in maintaining sustained reverberations within a network. The model shows two clear bifurcation points as delay is varied that transition the network into three different regions of operation. It also shows that the network can selectively remember patterns of input and sustain these patterns for as long as needed. This type of pattern storage is a viable model to explain working memory and processes similar to it.