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We investigate the role of the learning rate in a Kuramoto Model of coupledphase oscillators in which the coupling coefficients dynamically vary accordingto a Hebbian learning rule. According to the Hebbian theory, a synapse betweentwo neurons is strengthened if they are simultaneously co-active. Two stablesynchronized clusters in anti-phase emerge when the learning rate is largerthan a critical value. In such a fast learning scenario, the network eventuallyconstructs itself into an all-to-all coupled structure, regardless of initialconditions in connectivity. In contrast, when learning is slower than thiscritical value, only a single synchronized cluster can develop. Extending ouranalysis, we explore whether self-development of neuronal networks can beachieved through an interaction between spontaneous neural synchronization andHebbian learning. We find that self-development of such neural systems isimpossible if learning is too slow. Finally, we demonstrate that similar to theacquisition and consolidation of long-term memory, this network is capable ofgenerating and remembering stable patterns.

Learning-rate dependent clustering and self-development in a network of coupled phase oscillators