Stochastic Biomathematical Models

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

3. Neuronal Models

   1. Front Matter

      Pages 97-97

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   2. Stochastic Integrate and Fire Models: A Review on Mathematical Methods and Their Applications

      • Laura Sacerdote, Maria Teresa Giraudo

      Pages 99-148

   3. Stochastic Partial Differential Equations in Neurobiology: Linear and Nonlinear Models for Spiking Neurons

      • Henry C. Tuckwell

      Pages 149-173

   4. Deterministic and Stochastic FitzHugh–Nagumo Systems

      • Michèle Thieullen

      Pages 175-186

   5. Stochastic Modeling of Spreading Cortical Depression

      • Henry C. Tuckwell

      Pages 187-200

4. Back Matter

   Pages 201-206

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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.

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

• 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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