  Motivated by recent observations in neuronal systems we investigate
all-to-all networks of non-identical oscillators with adaptive coupling. The
adaptation models spike-timing-dependent plasticity in which the sum of the
weights of all incoming links is conserved. We find multiple phase-locked
states that fall into two classes: near-synchronized states and splay states.
Among the near-synchronized states are states that oscillate with a frequency
that depends only very weakly on the coupling strength and is essentially given
by the frequency of one of the oscillators, which is, however, neither the
fastest nor the slowest oscillator. In sufficiently large networks the adaptive
coupling is found to develop effective network topologies dominated by one or
two loops. This results in a multitude of stable splay states, which differ in
their firing sequences. With increasing coupling strength their frequency
increases linearly and the oscillators become less synchronized. The essential
features of the two classes of states are captured analytically in perturbation
analyses of the extended Kuramoto model used in the simulations.
