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Stochastic Biomathematical Models

with Applications to Neuronal Modeling

  • Book
  • © 2013

Overview

Editors:
  1. Mostafa Bachar

    1. College of Sciences, Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

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  2. Jerry Batzel

    1. Mathematics and Scientific Computing, University of Graz, Graz, Austria

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    You can also search for this editor in PubMed   Google Scholar

  3. Susanne Ditlevsen

    1. Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark

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  • Written by current leading experts in the field
  • Focus on interdisciplinary (physiological and biological) applications of stochastic methods Representation of key theoretical ideas but also clear and motivated examples of application and implementation issues
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2058)

Part of the book sub series: Mathematical Biosciences Subseries (LNMBIOS)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Methodology

    1. Front Matter

      Pages 1-1
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    2. Introduction to Stochastic Models in Biology

      • Susanne Ditlevsen, Adeline Samson
      Pages 3-35

    3. One-Dimensional Homogeneous Diffusions

      • Martin Jacobsen
      Pages 37-55

    4. A Brief Introduction to Large Deviations Theory

      • Gilles Wainrib
      Pages 57-72

    5. Some Numerical Methods for Rare Events Simulation and Analysis

      • Gilles Wainrib
      Pages 73-95

  4. Back Matter

    Pages 201-206
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Keywords

About this book

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.

Editors and Affiliations

  • College of Sciences, Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

    Mostafa Bachar

  • Mathematics and Scientific Computing, University of Graz, Graz, Austria

    Jerry Batzel

  • Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark

    Susanne Ditlevsen

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