Hybrid Automata and ε-Analysis on a Neural Oscillator
Alberto Casagrande, Tommaso Dreossi, Carla Piazza · Electronic Proceedings in Theoretical Computer Science · 2012
In this paper we propose a hybrid model of a neural oscillator, obtained by partially discretizing a well-known continuous model. Our construction points out that in this case the standard techniques, based on replacing sigmoids with step functions, is not satisfactory. Then, we study the hybrid model through both symbolic methods and approximation techniques. This last analysis, in particular, allows us to show the differences between the considered approximation approaches. Finally, we focus on approximations via epsilon-semantics, proving how these can be computed in practice.