Predicting Fluctuation-Induced Tipping in Nonlinear Networks

Marc Timme

Fluctuations prevail across complex networked systems from biology to engineering, perturb intrinsic system dynamics and induce non-equilibrium distributed responses. Responses to weak fluctuations are typically approximated by linear response theory, yet often fluctuations are strong and may induce tipping. Here we report nonlinear distributed fluctuation-responses emerging generically in nonlinear dynamical systems yet are absent from most text book examples. Moreover, at some critical (large) driving amplitude, responses diverge from a neighborhood of an original operating point – the system tips. As standard response theory fails to predict tipping amplitudes, even at arbitrarily high orders, we propose self-consistency conditions that capture the genuinely nonlinear response dynamics. Our approach uncovers a generic pondermomotive route to tipping where the fluctuations coact with system nonlinearities to move average responses towards tipping. The approach may help to quantitatively predict intrinsically nonlinear response dynamics as well as tipping points emerging at large driving amplitudes across non-autonomous dynamical systems. We highlight several application directions and a broad field of open theoretical, practical and methodological questions.