Hallucinogen persisting perception disorder in neuronal networks with adaptation.
We study the spatiotemporal dynamics of neuronal networks with spike frequency adaptation. In particular, we compare the effects of adaptation being either a linear or nonlinear function of neural activity. We find that altering parameters controlling the strength of synaptic connections in the network can lead to spatially structured activity suggestive of symptoms of hallucinogen persisting perception disorder (HPPD). First, we study how both networks track spatially homogeneous flickering stimuli, and find input is encoded as continuous at lower flicker frequencies when the networks synapses exhibit more net excitation. Mainly, we study instabilities of stimulus-driven traveling pulse solutions, representative of visual trailing phenomena common to HPPD patients. Visual trails are reported as discrete afterimages in the wake of a moving input. Thus, we analyze several solutions arising in response to moving inputs in both networks an ON state, stimulus-locked pulses, and traveling breathers. We find traveling breathers can arise in both networks when an input moves beyond a critical speed. These possible neural substrates of visual trails occur at slower speeds when the modulation of synaptic connectivity is increased.