Dynamics of model oscillatory neuronal networks with adaptive synaptic weights and structure

We study the dynamics of phase oscillator networks with variable coupling strength and structure that can represent oscillatory neuronal networks where the spiking dynamics, synaptic weights, and network structure influence each other. We model synaptic weight adaptation by spike-timing-dependent plasticity (STDP) with a longer time scale than neuronal spiking and structural plasticity (SP) that alters the network architecture by adding and eliminating synaptic contacts at a longer time scale than STDP. We study the steady-state dynamics of networks that can settle either in synchronized or desynchronized states. We show that a combination of SP and STDP (STDP+SP) allows for a synchronized state with fewer links than a network with STDP only. With non-identical units, STDP+SP leads to correlations between the oscillators’ natural frequencies and node degrees. In a desynchronized state, STDP+SP leads to a sparser network. In this way, adding SP strengthens both synchronized and desynchronized states. Using a desynchronizing coordinated reset stimulus and a periodic synchronizing stimulus, we show that a network of identical oscillators with STDP+SP may require stronger and longer stimulation to switch between the states compared to a network with STDP only. Furthermore, we confirmed the emergence of a correlation between a neuron’s firing rate and degree using a leaky integrate & fire model of neurons.