  We investigate the role of the learning rate in a Kuramoto Model of coupled
phase oscillators in which the coupling coefficients dynamically vary according
to a Hebbian learning rule. According to the Hebbian theory, a synapse between
two neurons is strengthened if they are simultaneously co-active. Two stable
synchronized clusters in anti-phase emerge when the learning rate is larger
than a critical value. In such a fast learning scenario, the network eventually
constructs itself into an all-to-all coupled structure, regardless of initial
conditions in connectivity. In contrast, when learning is slower than this
critical value, only a single synchronized cluster can develop. Extending our
analysis, we explore whether self-development of neuronal networks can be
achieved through an interaction between spontaneous neural synchronization and
Hebbian learning. We find that self-development of such neural systems is
impossible if learning is too slow. Finally, we demonstrate that similar to the
acquisition and consolidation of long-term memory, this network is capable of
generating and remembering stable patterns.
