This ebook applies methods from nonlinear dynamics to explore problems in neuroscience, utilizing modern mathematical approaches to decipher patterns of neuronal activity observed in experiments and models. It targets researchers eager to apply mathematics to significant neuroscience challenges, as well as neuroscientists interested in model creation and the mathematical and computational techniques for their analysis. The authors adopt a broad perspective, employing diverse methods to tackle and understand complex models of neurons and circuits. They integrate numerical, analytical, dynamical systems, and perturbation methods to present a contemporary approach to the model equations prevalent in neuroscience.
The ebook features extensive discussions on the role of noise, multiple time scales, and spatial interactions in generating the complex activity patterns found in experiments. Early chapters require only basic calculus and elementary differential equations, making them suitable as a foundational resource for a computational neuroscience course. Later chapters serve as a basis for graduate-level classes and current research in mathematical neuroscience. With numerous illustrations, chapter summaries, and hundreds of exercises inspired by biological issues involving computation and analysis, this book is a comprehensive tool for both learning and research. Bard Ermentrout is a Professor of Computational Biology and Mathematics at the University of Pittsburgh, while David Terman is a Professor of Mathematics at Ohio State University.
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