In mathematics, the master stability function is a tool used to analyse the stability of the synchronous state in a dynamical system consisting of many identical oscillators which are coupled together, such as the Kuramoto model.
The setting is as follows. Consider a system with
The coupling is defined by a coupling strength
It is assumed that the row sums
The master stability function is now defined as the function which maps the complex number
The synchronous state of the system of coupled oscillators is stable if the master stability function is negative at