Wilson, H. R. (1999) Spikes, Decisions & Actions: Dynamical Foundations of Neuroscience, Oxford University Press, Oxford UK. 324 pp.
This text is offered freely by the author at the http://cvr.yorku.ca/webpages/wilson.htm#book .
In the preface to the book the author offers a rationale for the study,
"There is one central reason why all neuroscientists and biopsychologists should be conversant with nonlinear dynamics. Nonlinear dynamics reveals and elucidates a range of phenomena that are simply inconceivable in the more mundane world of linear systems theory. Memory and forgetting, decision making, motor control, action potentials, and perhaps even free will and determinism can no longer be intelligently conceptualized without a basic understanding of nonlinear systems. At the deepest level, therefore, my decision to write this book was predicated on the belief that an understanding of brain function and behavior must be grounded in a conceptual framework informed by nonlinear dynamics.
At the web page in support of the text the author says, "The book is accompanied by a disk containing about 100 MatLab™ scripts that are intended to complement the text MatLab was chosen because the scripts will run on the Macintosh, UNIX, or Windows platforms." These are offered at the site.
The book itself is an excellent tour of models using differential equations and techniques with applications. Moreover, the motivation to study the mathematics is very rich with examples and references in which the mathematics is used in practice. While it could be a stretch to use it as a general differential equations course text it sure would be exciting for students interested in biology, neuroscience in particular.
The text is self-contained with respect to the mathematics and that is what makes it a potential differential equations course text and the first half of the book has rich examples, but also develops the mathematics and the techniques for analyzing differential equations. For example sample chapter titles are "First order linear differential equations" and "Two-dimensional systems and state space." The latter portion of the text is driven by neuroscience topics, e.g., "Swimming and traveling waves," in which the neural and motion equations for lamprey eels is developed.
Of course, the text, since it is free and online with complete MatLab resources can serve as a stand alone source of student reading and projects.
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