Optimal cost tuning of frustration: Achieving desired states in the Kuramoto-Sakaguchi model

There are numerous examples of studied real-world systems that can be described as dynamical characterized by individual phases and coupled in a network like structure. Within the framework oscillatory models, much attention has been devoted to Kuramoto model, which considers collection oscillators interacting through sinus function phase differences. In this paper, we draw on an extension called Kuramoto-Sakaguchi adds lag parameter each node. We construct general formalism allows compute set parameters may lead any configuration within linear approximation. particular, devote special cases full synchronization symmetric configurations. show natural frequencies, at steady state is equation continuous spectra solutions feasible. order quantify system's strain achieve particular configuration, define cost optimal minimizes it. Despite considering approximation obtained tuned for case enhance frequency nonlinear model well.