  We introduce the concept of synchronization bombs as large networks of
coupled heterogeneous oscillators that operate in a bistable regime and
abruptly transit from incoherence to phase-locking (or vice-versa) by adding
(or removing) one or a few links. Here we build a self-organized and stochastic
version of these bombs, by optimizing global synchrony with decentralized
information in a competitive link-percolation process driven by a local rule.
We find explosive fingerprints on the emerging network structure, including
frequency-degree correlations, disassortative patterns and a delayed
percolation threshold. We show that these bomb-like transitions can be designed
both in systems of Kuramoto -- periodic -- and R\"ossler -- chaotic --
oscillators and in a model of cardiac pacemaker cells. We analytically
characterize the transitions in the Kuramoto case by combining a precise
collective coordinates approach and the Ott-Antonsen ansatz. Furthermore, we
study the robustness of the phenomena under changes in the main parameters and
the unexpected effect of optimal noise in our model. Our results propose a
minimal self-organized mechanism of network growth to understand and control
explosive synchronization in adaptive biological systems like the brain and
engineered ones like power-grids or electronic circuits. From a theoretical
standpoint, the emergence of synchronization explosions and bistability induced
by localized structural perturbations -- without any fine-tuning of global
parameters -- joins explosive synchronization and percolation under the same
mechanistic framework.
