Optimizing Noisy Complex Systems Liable to Failure

Inspired by complex systems in social and industrial contexts, we consider a family of coupled diffusion processes modeling system components, and an associated system objective. Each process is inherently noisy, driven by a controllable drift, and fails upon reaching a critical state. Interdependence is captured via the global objective and the governing dynamics (correlated noise, cascading failures). Analytical and numerical calculations reveal that the optimal strategies to steer such systems so as to maximise the objective are highly coupled, depending strongly on the state of the entire system. Strikingly, they exhibit a rich set of bifurcations, describing qualitatively different strategies throughout the parameter space.