Selforganised pattern formation in non-local interacting neural fields

Classical selforganisation effects like pattern formation and phase transitions were observed in the human brain. The neural field model proposed by Wilson and Cowan (1973) allows a mathematical description for some of this phenomena, which might play an important role for the understanding of the human brain activity.

We study the dynamics of two-dimensional neural fields of activator-inhibitor-type and consider three types of external stimulation: homogeneous and stationary fields, homogeneous and oscillatory fields and localised excitation. Numerical simulations of the basic equations show interesting behaviors for the neural response, such as spatio-temporal pattern formation, frequency demultiplication, and travelling waves.