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We describe a direct constructive method of realising finite state input-dependent computations on an arbitrary directed graph. The constructed system has an excitable network attractor whose dynamics we illustrate with a number of examples. The resulting CTRNN has intermittent dynamics: trajectories spend long periods of time close to steady-state, with rapid transitions between states. Depending on parameters, transitions between states can either be<jats:italic>excitable<\/jats:italic>(inputs or noise needs to exceed a threshold to induce the transition), or<jats:italic>spontaneous<\/jats:italic>(transitions occur without input or noise). In the excitable case, we show the threshold for excitability can be made arbitrarily sensitive.<\/jats:p>","DOI":"10.1007\/s00422-021-00895-5","type":"journal-article","created":{"date-parts":[[2021,10,5]],"date-time":"2021-10-05T16:55:25Z","timestamp":1633452925000},"page":"519-538","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Excitable networks for finite state computation with continuous time recurrent neural networks"],"prefix":"10.1007","volume":"115","author":[{"given":"Peter","family":"Ashwin","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0654-6736","authenticated-orcid":false,"given":"Claire","family":"Postlethwaite","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,10,5]]},"reference":[{"issue":"4","key":"895_CR1","doi-asserted-by":"publisher","first-page":"1123","DOI":"10.1063\/1.1819625","volume":"14","author":"V Afraimovich","year":"2004","unstructured":"Afraimovich V, Zhigulin V, Rabinovich M (2004) On the origin of reproducible sequential activity in neural circuits. 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