Skip to main content Skip to local navigation
Home » Book


Spikes, Decisions & Actions:

Dynamical Foundations of Neuroscience

Hugh R. Wilson

Centre for Vision Research
York University of Toronto

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.

Please email any suggestions or typographical errors found to:

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

Spikes, Decisions & Actions
Corrections to the First Edition

p. 82, Eqn (6.16): right side of equation should read = 900 E12 (i.e., E1 should be squared).
p. 85, Eqn (6.19): upper right entry in matrix should be -5/(4t) rather than 0.
p. 87, next to last line: should read E2 = 1.
p. 91, Eqn (7.3): lower left entry in matrix should NOT include N. It should be: -S'k.
p. 91, paragraph below Eqn. (7.3): there should be a factor of 1/t multiplying all values of l.
p. 114: there should be a horizontal line marked F through the bottom left circle in the figure.
p. 147, Eqn (9.10): the last term in the dR/dt equation should be multiplied by the factor of 3.3, NOT 0.33.
p. 202: the program mentioned in the first line of problem #1 is EPSPinteractions.m. NOT EPEP…
p. 273, Eqn (15.48): the last term in the second equation should have (1 - p) in the denominator, not just p.
These are the only known error corrections at present.
If you find any additional corrections, please email me at: