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Tipping elements in the Earth System receive increased scientific attentionover the recent years due to their nonlinear behavior and the risks of abruptstate changes. While being stable over a large range of parameters, a tippingelement undergoes a drastic shift in its state upon an additional smallparameter change when close to its tipping point. Recently, the focus ofresearch broadened towards emergent behavior in networks of tipping elements,like global tipping cascades triggered by local perturbations. Here, we analyzethe response to the perturbation of a single node in a system that initiallyresides in an unstable equilibrium. The evolution is described in terms ofcoupled nonlinear equations for the cumulants of the distribution of theelements. We show that drift terms acting on individual elements and offsets inthe coupling strength are sub-dominant in the limit of large networks, and wederive an analytical prediction for the evolution of the expectation (i.e., thefirst cumulant). It behaves like a single aggregated tipping elementcharacterized by a dimensionless parameter that accounts for the network size,its overall connectivity, and the average coupling strength. The resultingpredictions are in excellent agreement with numerical data for Erd\"os-R\'enyi,Barab\'asi-Albert and Watts-Strogatz networks of different size and withdifferent coupling parameters.

Complex networks of interacting stochastic tipping elements: cooperativity of phase separation in the large-system limit