  Adaptation plays a fundamental role in shaping the structure of a complex
network and improving its functional fitting. Even when increasing the level of
synchronization in a biological system is considered as the main driving force
for adaptation, there is evidence of negative effects induced by excessive
synchronization. This indicates that coherence alone can not be enough to
explain all the structural features observed in many real-world networks. In
this work, we propose an adaptive network model where the dynamical evolution
of the node states towards synchronization is coupled with an evolution of the
link weights based on an anti-Hebbian adaptive rule, which accounts for the
presence of inhibitory effects in the system. We found that the emergent
networks spontaneously develop the structural conditions to sustain explosive
synchronization. Our results can enlighten the shaping mechanisms at the heart
of the structural and dynamical organization of some relevant biological
systems, namely brain networks, for which the emergence of explosive
synchronization has been observed.
