Coherent activity of two or many interconnected neurons is thought to play
important role in processing information in the central nervous system. Synchronous neural activity is believed to be part of many cognitive and sensory processing tasks such as feature binding, attention and memory construction. High levels of synchronization has been implicated in brain disorders like epilepsy, schizophrenia, Alzheimer's disease and Parkinson. Therefore, studying mechanisms underlying synchrony in the brain is of fundamental importance in understanding brain processes.
There has been little mathematical analysis of neural networks because the equations used to model these systems typically exhibit highly non-linear and stiff patterns. It is often difficult to make sense of the main events of neuronal dynamics from these models. In particular, in a network setting the question arises whether all the details described in the network models are required to comprehend the computation in large population of neurons. To gain intuitive insight into the dynamical properties of networks, by taking advantage of existence of different time scales in "spike generating" and modulatory current variables, we reduced the model to a biologically realistic discrete map involving most of the original system parameters to investigate the behavior of two layer excitatory-inhibitory oscillatory-synchronous neural networks for many different parameters as well as for many different network architectures including the ones that lead to lurching waves and irregular behaviors.
The analysis allows us derive explicit conditions in terms of the parameters in the original model for what a particular type of rhythmic activity exists It also allows us to compute the frequency of oscillations and speed of wave propagation.