  We study the capacity of Hodgkin-Huxley neuron in a network to change
temporarily or permanently their connections and behavior, the so called spike
timing-dependent plasticity (STDP), as a function of their synchronous
behavior. We consider STDP of excitatory and inhibitory synapses driven by
Hebbian rules. We show that the final state of networks evolved by a STDP
depend on the initial network configuration. Specifically, an initial
all-to-all topology envolves to a complex topology. Moreover, external
perturbations can induce co-existence of clusters, those whose neurons are
synchronous and those whose neurons are desynchronous. This work reveals that
STDP based on Hebbian rules leads to a change in the direction of the synapses
between high and low frequency neurons, and therefore, Hebbian learning can be
explained in terms of preferential attachment between these two diverse
communities of neurons, those with low-frequency spiking neurons, and those
with higher-frequency spiking neurons.
