Synchronization in coupled Morris-Lecar neurons with class I and class II excitability

In recent neuroscience, many researchers have claimed that synchronization of coupled neurons plays a very important role to code information in the brain. Neurons are classified into two types, class I and class II, by the difference of the onsets of the firing. These two types are confirmed by the physiologic experiments and it is very important to know how these differences affect synchronization. For mutual synchronization of two neurons, it is clarified by using the phase resetting curve (PRC) that class II neurons easily achieve synchronization [1]-[3]. Also for a large number of neurons with random connections, class II neurons present a good level of synchronization regardless of the connection topology [4]. Also for forced synchronization, class II neurons have advantage of acquiring synchronization [5]. However, Tsuji et al. showed that class I neurons have wider parameter regions of synchronous firing than those for class II neurons by detailed bifurcation analysis [6]. In this paper, we compare the parameter regions of inphase synchronization for the coupled Morris-Lecar(ML) neurons by a chemical synapse, when the values of the synaptic delay and the synaptic conductance are changed. The ML neuron model can be switched between class I and class II excitabilities by changing the value of one parameter [7]. Thus, in this paper, we use the ML model and compare the bifurcation structure for class I and class II by using the method [8] for analyzing the system with the synaptic delay.