With the physical limitations of current CMOS technology, it becomes necessary to design and develop new methods to perform simple and complex computations. Nature is efficient, so many in the scientific community attempt to mimic it when optimizing or creating new systems and devices. The human brain is looked to as an efficient computing device, inspiring strong interest in developing powerful computer systems that resemble its architecture and behavior such as neural networks. There is much research focusing on both circuit designs that behave like neurons and arrangement of these electromechanical neurons to compute complex operations.
It has been shown previously that the synchronization characteristics of neural oscillators can be used not only for primitive computation functions such as convolution but for complex non-Boolean computations. With strong interest in the research community to develop biologically representative neural networks, this dissertation analyzes and simulates biologically plausible networks, the four-dimensional Hodgkin-Huxley and the simpler two-dimensional Fitzhugh-Nagumo neural models, fashioned in winner-take-all neuronal networks. The synchronization behavior of these neurons coupled together is studied in detail. Different neural network topologies are considered including lateral inhibition and inhibition via a global interneuron. Then, this dissertation analyzes the winner-take-all behaviors, in terms of both firing rates and phases, of neuronal networks with different topologies. A technique based on phase response curve is suggested for the analysis of synchronization phase characteristics of winner-take-all networks. Simulations are performed to validate the analytical results. This study promotes the understanding of winner-take-all operations in biological neuronal networks and provides a fundamental basis for applications of winner-take-all networks in modern computing systems
