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.
Fred Brauer, PhD, University of British Columbia, Vancouver, Canada Christopher Kribs, PhD, University of Texas at Arlington, USA
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