Hybrid Automata and \epsilon-Analysis on a Neural Oscillator
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2012
- DOI:
- 10.48550/arXiv.1208.3852
- arXiv:
- arXiv:1208.3852
- Bibcode:
- 2012arXiv1208.3852C
- Keywords:
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- Computer Science - Computational Engineering;
- Finance;
- and Science;
- Computer Science - Logic in Computer Science;
- Computer Science - Symbolic Computation
- E-Print:
- In Proceedings HSB 2012, arXiv:1208.3151