Two dimensional synaptically generated traveling waves in a theta-neuron neural network

This paper extends some of the previous work on synaptically generated traveling waves from one dimension to two dimensions. Numerical simulations of networks of the so-called theta neurons were used for exploration of the existence, stability and the nature of these waves. The symmetric nature of the traveling waves was justi"ed and a numerical scheme for evaluating the velocity of the traveling waves was constructed. Adding adaptation in the network and imposing special initial conditions gave rise to spiral waves. Moreover, adding delays allowed the formation of the traveling lurching waves. Finally, direction for future work is suggested. 2001 Published by Elsevier Science B.V.