SYNCHRONIZED ACTION OF SYNAPTICALLY COUPLED CHAOTIC MODEL NEURONS

Experimental observations of the intracellular recorded electrical act ivity in individual neurons show that the temporal behavior is often c haotic We discuss both our own observations on a cell from the stomato gastric central pattern generator of lobster and earlier observations in other cells. In this paper we work with models of chaotic neurons, building on models by Hindmarsh and Rose for bursting, spiking activit y in neurons. The key feature of these simplified models of neurons is the presence of coupled slow and fast subsystems. We analyze the mode l neurons using the same tools employed in the analysis of our experim ental data. We couple two model neurons both electrotonically and elec trochemically in inhibitory and excitatory fashions. In each of these cases, we demonstrate that the model neurons can synchronize in phase and out of phase depending on the strength of the coupling. For normal synaptic coupling, we have a time delay between the action of one neu ron and the response of the other. We also analyze how the synchroniza tion depends on this delay. A rich spectrum of synchronized behaviors is possible for electrically coupled neurons and for inhibitory coupli ng between neurons. In synchronous neurons one typically sees chaotic motion of the coupled neurons. Excitatory coupling produces essentiall y periodic voltage trajectories, which are also synchronized. We displ ay and discuss these synchronized behaviors using two ''distance'' mea sures of the synchronization.