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What happens in our brain when we make a decision? What triggers a neuron to send out a signal? What is the neural code? This textbook for advanced undergraduate and beginning graduate students provides a thorough and up-to-date introduction to the fields of computational and theoretical neuroscience. It covers classical topics, including the Hodgkin-Huxley equations and Hopfield model, as well as modern developments in the field such as generalized linear models and decision theory. Concepts are introduced using clear step-by-step explanations suitable for readers with only a basic knowledge of differential equations and probabilities, and are richly illustrated by figures and worked-out examples. End-of-chapter summaries and classroom-tested exercises make the book ideal for courses or for self-study. The authors also give pointers to the literature and an extensive bibliography, which will prove invaluable to readers interested in further study.

Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition

Preface; Part I. Foundations of Neuronal Dynamics: 1. Introduction; 2. The Hodgkin-Huxley model; 3. Dendrites and synapses; 4. Dimensionality reduction and phase plane analysis; Part II. Generalized Integrate-and-Fire Neurons: 5. Nonlinear integrate-and-fire models; 6. Adaptation and firing patterns; 7. Variability of spike trains and neural codes; 8. Noisy input models: barrage of spike arrivals; 9. Noisy output: escape rate and soft threshold; 10. Estimating models; 11. Encoding and decoding with stochastic neuron models; Part III. Networks of Neurons and Population Activity: 12. Neuronal populations; 13. Continuity equation and the Fokker-Planck approach; 14. The integral-equation approach; 15. Fast transients and rate models; Part IV. Dynamics of Cognition: 16. Competing populations and decision making; 17. Memory and attractor dynamics; 18. Cortical field models for perception; 19. Synaptic plasticity and learning; 20. Outlook: dynamics in plastic networks; Bibliography; Index.