Emergent explosive synchronization in adaptive complex networks

Adaptation plays a fundamental role in shaping the structure of acomplex network and improving its functional fitting. Even whenincreasing the level of synchronization in a biological system isconsidered as the main driving force for adaptation, there is evidenceof negative effects induced by excessive synchronization. This indicatesthat coherence alone cannot be enough to explain all the structuralfeatures observed in many real-world networks. In this work, we proposean adaptive network model where the dynamical evolution of the nodestates toward synchronization is coupled with an evolution of the linkweights based on an anti-Hebbian adaptive rule, which accounts for thepresence of inhibitory effects in the system. We found that the emergentnetworks spontaneously develop the structural conditions to sustainexplosive synchronization. Our results can enlighten the shapingmechanisms at the heart of the structural and dynamical organization ofsome relevant biological systems, namely, brain networks, for which theemergence of explosive synchronization has been observed.