Multistability in a star network of Kuramoto-type oscillators with synaptic plasticity

We analyze multistability in a star-type network of phase oscillators with coupling weights governed by phase-difference-dependent plasticity. It is shown that a network with N leaves can evolve into [Formula: see text] various asymptotic states, characterized by different values of the coupling strength between the hub and the leaves. Starting from the simple case of two coupled oscillators, we develop an analytical approach based on two small parameters [Formula: see text] and [Formula: see text], where [Formula: see text] is the ratio of the time scales of the phase variables and synaptic weights, and [Formula: see text] defines the sharpness of the plasticity boundary function. The limit [Formula: see text] corresponds to a hard boundary. The analytical results obtained on the model of two oscillators are generalized for multi-leaf star networks. Multistability with [Formula: see text] various asymptotic states is numerically demonstrated for one-, two-, three- and nine-leaf star-type networks.