Mathematical models can be used to meet many of the challenges and opportunities offered by modern biology. The description of biological phenomena requires a range of mathematical theories. This is the case particularly for the emerging field of systems biology. Mathematical Methods in Biology and Neurobiology introduces and develops these mathematical structures and methods in a systematic manner. It studies: • discrete structures and graph theory • stochastic processes • dynamical systems and partial differential equations • optimization and the calculus of variations. The biological applications range from molecular to evolutionary and ecological levels, for example: • cellular reaction kinetics and gene regulation • biological pattern formation and chemotaxis • the biophysics and dynamics of neurons • the coding of information in neuronal systems • phylogenetic tree reconstruction • branching processes and population genetics • optimal resource allocation • sexual recombination • the interaction of species. Written by one of the most experienced and successful authors of advanced mathematical textbooks, this book stands apart for the wide range of mathematical tools that are featured. It will be useful for graduate students and researchers in mathematics and physics that want a comprehensive overview and a working knowledge of the mathematical tools that can be applied in biology. It will also be useful for biologists with some mathematical background that want to learn more about the mathematical methods available to deal with biological structures and data.

The lack of scientists equally trained and prepared to understand both mathematics and biology/medicine hampers the development and application of computer simulation methods in biology and neurogastrobiology. Currently, there are no texts for navigating the extensive and intricate field of mathematical and computational modeling in neurogastrobiology. This book bridges the gap between mathematicians, computer scientists and biologists, and thus assists in the study and analysis of complex biological phenomena that cannot be done through traditional in vivo and in vitro experimental approaches.The book recognizes the complexity of biological phenomena under investigation and treats the subject matter with a degree of mathematical rigor. Special attention is given to computer simulations for interpolation and extrapolation of electromechanical and chemoelectrical phenomena, nonlinear self-sustained electromechanical wave activity, pharmacological effects including co-localization and co-transmission by multiple neurotransmitters, receptor polymodality, and drug interactions.Mathematical Modeling and Simulation in Enteric Neurobiology is an interdisciplinary book and is an essential source of information for biologists and doctors who are interested in knowing about the role and advantages of numerical experimentation in their subjects, as well as for mathematicians who are interested in exploring new areas of applications.

Arising from several courses taught by the authors, this book provides a needed overview illustrating how dynamical systems and computational analysis have been used in understanding the types of models that come out of neuroscience.

Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in stochastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and stochastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in stochastic neurobiological models, a review of mathematical methods for stochastic neuronal integrate-and-fire models, stochastic partial differential equation models in neurobiology, and stochastic modeling of spreading cortical depression.

Mathematics for Neuroscientists, Second Edition, presents a comprehensive introduction to mathematical and computational methods used in neuroscience to describe and model neural components of the brain from ion channels to single neurons, neural networks and their relation to behavior. The book contains more than 200 figures generated using Matlab code available to the student and scholar. Mathematical concepts are introduced hand in hand with neuroscience, emphasizing the connection between experimental results and theory. - Fully revised material and corrected text - Additional chapters on extracellular potentials, motion detection and neurovascular coupling - Revised selection of exercises with solutions - More than 200 Matlab scripts reproducing the figures as well as a selection of equivalent Python scripts

Mathematical Neuroscience is a book for mathematical biologists seeking to discover the complexities of brain dynamics in an integrative way. It is the first research monograph devoted exclusively to the theory and methods of nonlinear analysis of infinite systems based on functional analysis techniques arising in modern mathematics. Neural models that describe the spatio-temporal evolution of coarse-grained variables—such as synaptic or firing rate activity in populations of neurons —and often take the form of integro-differential equations would not normally reflect an integrative approach. This book examines the solvability of infinite systems of reaction diffusion type equations in partially ordered abstract spaces. It considers various methods and techniques of nonlinear analysis, including comparison theorems, monotone iterative techniques, a truncation method, and topological fixed point methods. Infinite systems of such equations play a crucial role in the integrative aspects of neuroscience modeling. - The first focused introduction to the use of nonlinear analysis with an infinite dimensional approach to theoretical neuroscience - Combines functional analysis techniques with nonlinear dynamical systems applied to the study of the brain - Introduces powerful mathematical techniques to manage the dynamics and challenges of infinite systems of equations applied to neuroscience modeling