Abstract
We investigate synchronization in neuronal networks with a small-world-like structure. Inhibitory connected neurons are considered. In a previous study, we found an interesting quasi-periodic solution such that neurons are classified into three groups: two groups with distinct firing rates and one group with only subthreshold oscillations. In this paper, we study its generation mechanism in the smallest system in which we can reconnect one synapse. As a result, we obtain the following mechanism: (1) non-uniformity of the firing frequency appears as a result of asymmetrical coupling, (2) neurons with a higher firing frequency suppress neurons with a lower firing frequency for an appropriate coupling coefficient, (3) three clustered states, that is, neurons with firing frequencies A and B (A/B is irrational) and neurons that do not fire, are generated. We also confirm this mechanism in a large population.
