Dynamical Systems for Biological Modeling: An Introduction, 1st Edition (Hardback) book cover

Dynamical Systems for Biological Modeling

An Introduction, 1st Edition

By Fred Brauer, Christopher Kribs

Chapman and Hall/CRC

478 pages | 220 B/W Illus.

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pub: 2015-12-22
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Description

Dynamical Systems for Biological Modeling: An Introduction prepares both biology and mathematics students with the understanding and techniques necessary to undertake basic modeling of biological systems. It achieves this through the development and analysis of dynamical systems.

The approach emphasizes qualitative ideas rather than explicit computations. Some technical details are necessary, but a qualitative approach emphasizing ideas is essential for understanding. The modeling approach helps students focus on essentials rather than extensive mathematical details, which is helpful for students whose primary interests are in sciences other than mathematics need or want.

The book discusses a variety of biological modeling topics, including population biology, epidemiology, immunology, intraspecies competition, harvesting, predator-prey systems, structured populations, and more.

The authors also include examples of problems with solutions and some exercises which follow the examples quite closely. In addition, problems are included which go beyond the examples, both in mathematical analysis and in the development of mathematical models for biological problems, in order to encourage deeper understanding and an eagerness to use mathematics in learning about biology.

Table of Contents

ELEMENTARY TOPICS

Introduction to Biological Modeling

The Nature and Purposes of Biological Modeling

The Modeling Process

Types of Mathematical Models

Assumptions, Simplifications, and Compromises

Scale and Choosing Units

Difference Equations (Discrete Dynamical Systems)

Introduction to Discrete Dynamical Systems

Graphical Analysis

Qualitative Analysis and Population Genetics

Intraspecies Competition

Harvesting

Period Doubling and Chaos

Structured Populations

Predator-Prey Systems

First-Order Differential Equations (Continuous Dynamical Systems)

Continuous-Time Models and Exponential Growth

Logistic Population Models

Graphical Analysis

Equations and Models with Variables Separable

Mixing Processes and Linear Models

First-Order Models with Time Dependence

Nonlinear Differential Equations

Qualitative Analysis Tools

Harvesting

Mass-Action Models

Parameter Changes, Thresholds, and Bifurcations

Numerical Analysis of Differential Equations

MORE ADVANCED TOPICS

Systems of Differential Equations

Graphical Analysis: The Phase Plane

Linearization of a System at an Equilibrium

Linear Systems with Constant Coefficients

Qualitative Analysis of Systems

Topics in Modeling Systems of Populations

Epidemiology: Compartmental Models

Population Biology: Interacting Species

Numerical Approximation to Solutions of Systems

Systems with Sustained Oscillations and Singularities

Oscillations in Neural Activity

Singular Perturbations and Enzyme Kinetics

HIV - An Example from Immunology

Slow Selection in Population Genetics

Second-Order Differential Equations: Acceleration

APPENDICES

An Introduction to the Use of MapleTM

Taylor’s Theorem and Linearization

Location of Roots of Polynomial Equations

Stability of Equilibrium of Difference Equations

Answers to Selected Exercises

Bibliography

About the Authors

Fred Brauer, PhD, University of British Columbia, Vancouver, Canada

Christopher Kribs, PhD, University of Texas at Arlington, USA

About the Series

Advances in Applied Mathematics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations