Stochastic Biomathematical Models

with Applications to Neuronal Modeling

  • Mostafa Bachar
  • Jerry Batzel
  • Susanne Ditlevsen

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

Also part of the Mathematical Biosciences Subseries book sub series (LNMBIOS, volume 2058)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Methodology

    1. Front Matter
      Pages 1-1
    2. Susanne Ditlevsen, Adeline Samson
      Pages 3-35
    3. Martin Jacobsen
      Pages 37-55
  3. Neuronal Models

  4. Back Matter
    Pages 201-206

About this book

Introduction

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.

Keywords

60Gxx, 92C20, 37N25, 92Bxx Spreading cortical depression Stochastic Integrate-and-Fire Models Stochastic differential equation models in biology Stochastic partial differential equations in neurobiology

Editors and affiliations

  • Mostafa Bachar
    • 1
  • Jerry Batzel
    • 2
  • Susanne Ditlevsen
    • 3
  1. 1.College of Sciences, Department of MathematicsKing Saud UniversityRiyadhSaudi Arabia
  2. 2.Mathematics and Scientific ComputingUniversity of GrazGrazAustria
  3. 3.Department of Mathematical SciencesUniversity of CopenhagenCopenhagenDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-32157-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-32156-6
  • Online ISBN 978-3-642-32157-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book