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

Autor(es)

Kohler, Jan ^{[1, 2]} ; Wunderling, Nico ^{[3, 4, 2]} ; Donges, Jonathan F. ^{[5, 2]} ; Vollmer, Juergen ^[1]

Afiliação do(s) autor(es)

^[1] Univ Leipzig, Inst Theoret Phys, D-04103 Leipzig - Germany

^[2] Potsdam Inst Climate Impact Res, Leibniz Assoc, Earth Syst Anal, D-14473 Potsdam - Germany

^[3] Humboldt Univ, Dept Phys, D-12489 Berlin - Germany

^[4] Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam - Germany

^[5] Stockholm Univ, Stockholm Resilience Ctr, S-10691 Stockholm - Sweden

• Tipo de documento: Artigo Científico
• Fonte: Physical Review E; v. 104, n. 4 OCT 4 2021.
• Citações Web of Science: 0

Resumo

Tipping elements in the Earth system have received increased scientific attention over recent years due to their nonlinear behavior and the risks of abrupt state changes. While being stable over a large range of parameters, a tipping element undergoes a drastic shift in its state upon an additional small parameter change when close to its tipping point. Recently, the focus of research broadened towards emergent behavior in networks of tipping elements, like global tipping cascades triggered by local perturbations. Here, we analyze the response to the perturbation of a single node in a system that initially resides in an unstable equilibrium. The evolution is described in terms of coupled nonlinear equations for the cumulants of the distribution of the elements. We show that drift terms acting on individual elements and offsets in the coupling strength are subdominant in the limit of large networks, and we derive an analytical prediction for the evolution of the expectation (i.e., the first cumulant). It behaves like a single aggregated tipping element characterized by a dimensionless parameter that accounts for the network size, its overall connectivity, and the average coupling strength. The resulting predictions are in excellent agreement with numerical data for Erdos-Renyi, Barabasi-Albert, and Watts-Strogatz networks of different size and with different coupling parameters. (AU)

• Processo FAPESP: 15/50122-0 - Fenômenos dinâmicos em redes complexas: fundamentos e aplicações
• Beneficiário: Elbert Einstein Nehrer Macau
• Modalidade de apoio: Auxílio à Pesquisa - Temático