Elsevier S & T

Dynamical Models in Biology

Farkas, Miklós

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Table of contents
  • Dynamical Models in Biologyiii
  • Copyright Pageiv
  • Contentsix
  • Prefacevii
  • Chapter 1. Discrete Population Models1
  • 1.1 Nonoverlapping Generations and Discrete Time Models1
  • 1.2 Population with Age Structure12
  • Chapter 2. Population Dynamics in Continuous time17
  • 2.1 The Logistic Equation and Human Demography17
  • 2.2 Two Interacting Species-Predator and Prey20
  • 2.3 Two Interacting Species-Competition and Cooperation30
  • 2.4 More Species38
  • 2.5 More Realism48
  • Chapter 3. Epidemics63
  • 3.1 The Spread of Diseases and Susceptibles/Infectives/Removed Models63
  • 3.2 Sexually Transmitted Diseases67
  • 3.3 A Model of Pair Formation69
  • 3.4 The Spread of Epidemics in Space73
  • Chapter 4. Evolution And population Genetics79
  • 4.1 The Phase Space of Genotypes and the Hardy-Weinberg Law79
  • 4.2 Equations of Selection, Recombination, and Mutation83
  • 4.3 The Origins of Life and Eigen's Hypercycle91
  • 4.4 The Immune System98
  • Chapter 5. Morphogenesis And Pattern Formation105
  • 5.1 Modeling the Embryo-Thom's Catastrophe Theory105
  • 5.2 Animal Hide and Shell Patterns114
  • Appendix 1. Discrete Mathematics125
  • A1.1 Linear Algebra125
  • A1.2 One-Dimensional Discrete Semiflows129
  • A1.3 Discrete Dynamical Systems136
  • A1.4 Branching Processes139
  • Appendix 2. Ordinary Differential Equations143
  • A2.1 Basic Facts143
  • A2.2 Stability146
  • A2.3 Bifurcations151
  • Appendix 3. Partial Differential Equations157
  • A3.1 First-Order Linear Equations157
  • A3.2 Reaction-Diffusion Equations161
  • A3.3 Turing Bifurcation164
  • Appendix 4. Riemannian Geometry171
  • A4.1 Local Riemannian Geometry171
  • A4.2 Shahshahani's Metric176
  • References179
  • Index184
Book details
  • Vendor Elsevier S & T
  • SKU 9780122491030R120
  • ISBN-13 9780080530604
  • Author Farkas, Miklós
  • Category Mathematics
  • Subject Applied

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* A 'down-to-earth' introduction to the growing field of modern mathematical biology
* Also includes appendices which provide background material that goes beyond advanced calculus and linear algebra