Chimera state and route to explosive synchronization

Transition to explosive synchronization is exhibited in networks of Kuramoto oscillators with a positive correlation between the oscillator dynamics and their inner topological structure encoded in the vertex degrees relations, shedding a light over the explosive critical phenomena. Here we study emergence of chimera states for the large amplitude oscillations when degree-frequency correlation is established only for the vertices with the highest degrees. For the strong coupling regime no simultaneous coexistence of coherence and incoherence signatures is observed. The connection between the network dynamics and the range and strength of coupling is elucidated through extensive analytical investigation, presenting realistic simulations of a scale-free neural network of Caenorhabditis elegans.