The official guide to the Brain Dynamics Toolbox The Brain Dynamics Toolbox is open-source software for simulating non-linear dynamical systems in Matlab. It is intended for students and researchers in computational neuroscience but can be applied to any domain. It specifically solves initial-value problems in systems of Ordinary Differential Equations (ODEs), Delay Differential Equations (DDEs) and Stochastic Differential Equations (SDEs). Each of which can be extended to a system of Partial Differential Equations (PDEs). The toolbox allows new dynamical systems to be rapidly prototyped and explored in an intuitive graphical application. Its hub-and-spoke software architecture allows interchangeable solver algorithms and plotting tools to be applied with no additional programming effort. Large-scale simulations can be run in user-defined scripts and the code for the model can be published independently of the toolbox.