Mathematical Concepts in Single-Neuron Dynamics

1. Auflage 2026
ISBN: 978-1-041-23819-5
Verlag: Taylor & Francis Ltd

Buch, Englisch, 136 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 372 g

Reihe: The Mathematical Concepts in Science Series

This book is designed as an introduction to neural dynamics through an intuitive exploration of fundamental "dynamic motifs"— the recurring dynamical concepts essential for understanding computational neuroscience. This concise, hands-on guide bridges the gap between mathematics and neuroscience, providing clear explanations of the key dynamical systems concepts that appear repeatedly in the computational/mathematical neuroscience literature.

Key Features:

• Geometric and intuitive descriptions that minimize mathematical formality while preserving clarity Interactive "Explorations" that reinforce concepts through computer-based exercises Complete solutions to all Explorations, allowing for self-guided learning

• Accessible approach suitable for both experimental neuroscientists and mathematicians

• Focused coverage of essential concepts that serve as building blocks for understanding complex neural models

This book serves as an ideal entry point into computational neuroscience for two distinct audiences: experimental neuroscientists seeking to understand computational techniques for collaboration and mathematicians or mathematics students looking to apply their knowledge to neuroscience. Through its unique combination of concise text and hands-on exploration, readers will quickly develop the knowledge and skills needed to navigate the computational neuroscience literature with confidence.

Zielgruppe

Postgraduate and Professional Practice & Development

Autoren/Hrsg.

Bertram, Richard

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

1 Introduction. 2 Excitability. 3 Bistability. 4 Saddle-node bifurcations. 5 Periodicity. 6 Coalescence of stable and unstable limit cycles. 7 The birth/death of tonic spiking with zero frequency. 8 Bursting oscillations. 9 Mean field models. 10 Additional resources. 11 Appendices. 12 Solutions to Explorations.

Über Autor(innen)

Richard Bertram is a Distinguished Research Professor at Florida State University. He is the director of Biomathematics in the Mathematics department, and is a member of the interdisciplinary programs in Molecular Biophysics and Neuroscience. His research is in neuroscience and endocrinology, where he and his lab use mathematics and computer simulations to understand experimental data and design new experiments. He is on the editorial boards of Biophysical Journal, the Bulletin of Mathematical Biology, and the SIAM Journal on Life Sciences and he serves on the board of directors of the Society for Mathematical Biology.