This work concerns the long-term collective excitability properties and the statistical analysis of the critical events displayed by a recently introduced spatiotemporal many-body model, proposed as a new paradigm for Artificial Life. Numerical simulations show that excitable collective structures emerge in the form of dynamic networks, created by bursts of spatiotemporal activity (avalanches) at the edge of a synchronization phase transition. The spatiotemporal dynamics is portraited by a movie and quantified by time varying collective parameters, showing that the dynamic networks undergo a “life cycle,” made of self-creation, homeostasis, and self-destruction. The power spectra of the collective parameters show 1/ f power law tails. The statistical properties of the avalanches, evaluated in terms of size and duration, show power laws with characteristic exponents in agreement with those values experimentally found in the neural networks literature. The mechanism underlying avalanches is argued in terms of local-to-collective excitability. The connections that link the present work to self-organized criticality, neural networks, and Artificial Life are discussed.