Hybrid Systems Neuroscience

We define the field of hybrid systems neuroscience as the reformulation of hybrid system models, analysis tools, and control schemes for neuronal systems. The field of hybrid systems has been built upon the theories of control and computer science. It has inherited control paradigms-including switching control systems and variable structure systems-originally designed for engineering problems, mainly in the areas of mechanical and electrical systems. The automated verification of hybrid systems has inherited computational paradigms originally designed for software systems or programs. The mixture has facilitated solutions to complex dynamical problems. However, the application of these paradigms to neuroscience cannot follow the orthodoxy of control and computational theories, and a new viewpoint is needed to model and analyze the complex and unique behaviors of brain networks. Under the hybrid systems neuroscience framework, we propose new concepts like switching dominance, self-organizing neuronal interdependent control (SONIC) or driver control neurons, and a new interpretation of hybrid automata. We illustrate these ideas in a novel working memory network model, which unifies the influence of dopamine, basal ganglia-thalamo-cortical circuits, and the generation of subcortical background oscillations.