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 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.

References in corpus (2)

• Thermodynamic limit of the first-order phase transition in the Kuramoto model
• Self-organization of feedforward structure and entrainment in excitatory neural networks with spike-timing-dependent plasticity

Cited by in corpus (10)

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• Complex macroscopic behavior in systems of phase oscillators with adaptive coupling
• Cyclops states in repulsive Kuramoto networks: the role of higher-order coupling
• Amplification of explosive width in complex networks
• Filippov trajectories and clustering in the Kuramoto model with singular couplings
• Dynamical equivalence between Kuramoto models with first- and higher-order coupling
• Effects of Synaptic and Myelin Plasticity on Learning in a Network of Kuramoto Phase Oscillators
• Path-dependent Dynamics Induced by Rewiring Networks of Inertial Oscillators