1st Edition

Dynamical Systems for Biological Modeling An Introduction

492 Pages 220 B/W Illustrations

by Chapman & Hall

492 Pages 220 B/W Illustrations

by Chapman & Hall

492 Pages

by Chapman & Hall

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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,... Read more

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 Maple^TM

Taylor’s Theorem and Linearization

Location of Roots of Polynomial Equations

Stability of Equilibrium of Difference Equations

Answers to Selected Exercises

Bibliography