So, PaulLuke, Tanushree2014-08-282014-08-282013-08https://hdl.handle.net/1920/8780Collective behavior in neural networks has often been used as an indicator of communication between different brain areas. These collective synchronization and desynchronization patterns are also considered an important feature in understanding normal and abnormal brain function. To understand the emergence of these collective patterns, I create an analytic model that identifies all such macroscopic steady-states attainable by a network of Type-I neurons. This network, whose basic unit is the model ``theta'' neuron, contains a mixture of excitable and spiking neurons coupled via a smooth pulse-like synapse. Applying the Ott-Antonsen reduction method in the thermodynamic limit, I obtain a low-dimensional evolution equation that describes the asymptotic dynamics of the macroscopic mean field of the network. This model can be used as the basis in understanding more complicated neuronal networks when additional dynamical features are included.152 pagesenCopyright 2013 Tanushree LukePhysicsChaosDriver-Response SystemMultipopulationNetworkNonlinear DynamicsTheta NeuronDissertation