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The behaviour of saccades matches that of the slow\u2013fast model of actions originally proposed by Zeeman. Here, we extend Zeeman\u2019s model by incorporating an accumulator that represents the increase in certainty of the presence of a target, together with an integrator that converts a velocity command to a position command. The saccadic behaviour of several foveate species, including human, rhesus monkey and mouse, is replicated by the augmented model. Predictions of the linear stability of the saccadic system close to equilibrium are made, and it is shown that these could be tested by applying state-space reconstruction techniques to neurophysiological recordings. Moreover, each model equation describes behaviour that can be matched to specific classes of neurons found throughout the oculomotor system, and the implication of the model is that build-up, burst and omnipause neurons are found throughout the oculomotor pathway because they constitute the simplest circuit that can produce the motor commands required to specify the trajectories of motor actions.<\/jats:p>","DOI":"10.1007\/s00422-020-00845-7","type":"journal-article","created":{"date-parts":[[2020,9,30]],"date-time":"2020-09-30T07:03:56Z","timestamp":1601449436000},"page":"519-532","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Slow\u2013fast control of eye movements: an instance of Zeeman\u2019s model for an action"],"prefix":"10.1007","volume":"114","author":[{"given":"Richard A.","family":"Clement","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9320-5958","authenticated-orcid":false,"given":"Ozgur E.","family":"Akman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,9,30]]},"reference":[{"key":"845_CR1","doi-asserted-by":"crossref","first-page":"1772","DOI":"10.1007\/s002210050229","volume":"117","author":"RV Abadi","year":"1997","unstructured":"Abadi RV, Broomhead DS, Clement RA, Whittle JP, Worfolk R (1997) Dynamical systems analysis: a new method of analysing congenital nystagmus waveforms. 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