title: Learning-rate-dependent clustering and self-development in a network of coupled phase oscillators.
abstract: 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 coactive. Two stable synchronized clusters in antiphase 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.
authors.affiliation: Department of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA.
authors.forename: Ritwik K
authors.initials: RK
authors.lastname: Niyogi
authors.forename: L Q
authors.initials: LQ
authors.lastname: English
mesh_terms: D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D016000:Cluster Analysis; D003198:Computer Simulation; D006801:Humans; D007858:Learning / Q000502:physiology; D008568:Memory; D008954:Models, Biological; D015233:Models, Statistical; D008962:Models, Theoretical; D009415:Nerve Net; D009474:Neurons / Q000378:metabolism; D016011:Normal Distribution; D009991:Oscillometry / Q000379:methods*