Titlebook: Mathematical Tools for Neuroscience; A Geometric Approach Richard A. Clement Book 2022 The Editor(s) (if applicable) and The Author(s), und

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Mind and Brain,tes of the state of the system as its behaviour changes. Whilst expanding on this argument, the opportunity is taken to introduce the basic terminology of dynamical systems theory and linear algebra that will recur throughout the book.

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Appendix: Background Material, developed to sort this type of problem out. Of course brains developed to handle more than just the problem of who sits where in front of the fire. The top cat, in terms of the one who gets what it wants, will have the largest repertoire of behaviours so it can counter the greatest range of situations that the world throws at it.

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Brain and Body,motor neural integrator. The linear approach is extended to simple nonlinear behaviour, using the larynx as an example. Nonlinearities lead to a greater range of behaviours of which heteroclinic cycles form one example.

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Analysis of Experimental Measurements,lues at the fixed points of the system, just as if the equations for a model of the system were available. The eye movement disorder of nystagmus is used as an example of this approach. In addition to the local analysis, topological data analysis can be used to obtain a description of the overall structure of the manifold of the dynamical system.

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978-3-030-98497-7The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Mathematical Tools for Neuroscience978-3-030-98495-3Series ISSN 2195-1934 Series E-ISSN 2195-1942

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