Dynamical Foundations of Neuroscience
by
Oxford University Press
Excerpts from the Preface:
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.
Spikes, Decisions & Actions is intended for three audiences: advanced undergraduates in neuroscience or physiological psychology, graduate students, and professionals in these areas who wish to develop neural simulations relevant to their own interests.
The book is accompanied by a disk containing about 100 MatLab™ scripts that are intended to complement the text. These simulations will help to solidify and elucidate analytic results and concepts derived in the text, and they should also enhance the utility of the book for self-study. Beyond this, their inclusion brings the book closer to the realities of research in theoretical neuroscience, where a combination of analysis and simulation is to be found in much of the best work. MatLab was chosen because the scripts will run on the Macintosh, UNIX, or Windows platforms.
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Table of Contents
Introduction 1
First order linear differential equations 13
Two-dimensional systems and state space 28
Higher dimensional linear systems 48
Approximation & simulation 60
Nonlinear dynamics & bifurcations 72
Computation by excitatory & inhibitory networks 88
Nonlinear oscillations 116
Action potentials & limit cycles 136
Neural adaptation & bursting 156
Neural Chaos 173
Synapses & synchrony 186
Swimming & traveling waves 205
Lyapunov functions & memory 223
Diffusion & dendrites 251
Nonlinear dynamics and brain function 279
Appendix: MatLab & the MatLab scripts 287
References 291
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