Spontaneous and evoked activity in extended neural populations with gamma-distributed spatial interactions and transmission delay

The spatiotemporal dynamics of neural activity are studied using an integro-differential model of spatially extended neuronal ensembles. The model includes both synaptic and axonal propagation delay while spatial synaptic connectivities are represented by gamma distributions. This family of connectivity kernels has been observed experimentally and covers the cases of divergent, finite, and negligible self-connections. We give conditions for stationary and non-stationary instabilities for gamma-distributed kernels, which can be formulated in terms of the mean spatial interaction ranges and the mean spatial interaction times. We present novel mechanisms for Turing patterns and traveling waves, which result from the special shape of the gamma-distributed interactions. We give a numerical study of the propagation of evoked spatiotemporal response activity caused by short local stimuli, and reveal maximum response activity after the mean interaction time. This maximum occurs at a distance from stimulus offset location, which is equal to the mean interaction range.