Dynamical Systems for Biological Modeling : An Introduction (Hardcover)

ELEMENTARY TOPICSIntroduction to Biological ModelingThe 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 GeneticsIntraspecies CompetitionHarvestingPeriod Doubling and ChaosStructured PopulationsPredator-Prey SystemsFirst-Order Differential Equations (Continuous Dynamical Systems)Continuous-Time Models and Exponential GrowthLogistic Population ModelsGraphical AnalysisEquations and Models with Variables SeparableMixing Processes and Linear ModelsFirst-Order Models with Time DependenceNonlinear Differential Equations Qualitative Analysis ToolsHarvestingMass-Action ModelsParameter Changes, Thresholds, and Bifurcations Numerical Analysis of Differential EquationsMORE ADVANCED TOPICSSystems of Differential EquationsGraphical Analysis: The Phase Plane Linearization of a System at an Equilibrium Linear Systems with Constant Coefficients Qualitative Analysis of SystemsTopics 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: AccelerationAPPENDICESAn 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 ExercisesBibliography