Georges Habib (Lebanese University, Beirut)
Caroline Wormell (University of Sydney and SFB visiting PhD research fellow)
Many physical problems, most importantly the quantification of climate change, involve estimating the response of a deterministic chaotic dynamical system's statistical equilibrium to perturbations in the dynamics. If the equilibrium varies differentiably with the perturbation, it is possible to compute a Taylor expansion of this response from only the unperturbed dynamics of the system. Many practitioners working with high-dimensional complex systems assume the differentiability requirement holds, at least for "large-scale" observables: however, theoretical work has shown that it fails for even very simple chaotic systems such as the logistic map. To understand this discrepancy, we analyse model systems consisting of large weakly-coupled networks of chaotic subsystems that may individually have a non-differentiable response. We derive reduced large-scale dynamics, and show that under physically reasonable assumptions the response of the large-scale observables is differentiable.
(Joint work with Georg Gottwald)