Effects of time delay on synchronization and firing patterns in coupled neuronal systems

Synchronization and firing patterns of neurons play a significant role in neural signal encoding and transduction of information processing of nervous systems. For real neurons, the signal transmission delay is inherent due to finite propagation speed of action potentials through axons, as well as both dendritic and synaptic processing. Time delay is universal and inevitable, and results in complex dynamical behavior, such as multistability and bifurcations leading to chaos. In this chapter, the authors provide a survey of some recent developments on the effects of time delay on synchronization and firing patterns in coupled neuronal systems. Basic concepts of firing patterns of neurons and complete and phase synchronization of oscillators are introduced. Synchronization and firing patterns in electrically coupled neurons as well as inhibitory and excitatory delayed synapses with time delay are presented. Delay effects on spatiotemporal dynamics of coupled neuronal activities are discussed. Some well-known neuron models are also included for benefit of the readers.