Mathematical Biology
1st Edition
Published on 9. March 2013
XIV, 770 pages
978-3-662-08539-4 (ISBN)
Description
Mathematical biology - the use of mathematical ideas and
models in the biosciences - is a fast growing, very exciting
and increasingly important inderdisciplinary field. This
textbook is an account of some of the major techniques and
models used and of some genuine practical applications drawn
from current areas of research interest in, for example,
population ecology, developmental biology, physiology,
epidemiology and evolution. It provides the reader with a
thorough background, sufficient to start genuine
interdisciplinary collaborative reserach with biomedical
scientists.
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James D. Murray
Mathematical Biology
Book
04/2013
1st Edition
Springer
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Content
1. Continuous Population Models for Single Species.- 2. Discrete Population Models for a Single Species.- 3. Continuous Models for Interacting Populations.- 4. Discrete Growth Models for Interacting Populations.- 5. Reaction Kinetics.- 6. Biological Oscillators and Switches.- 7. Belousov-Zhabotinskii Reaction.- 8. Perturbed and Coupled Oscillators and Black Holes.- 9. Reaction Diffusion, Chemotaxis and Non-local Mechanisms.- 10. Oscillator Generated Wave Phenomena and Central Pattern Generators.- 11. Biological Waves: Single Species Models.- 12. Biological Waves: Multi-species Reaction Diffusion Models.- *13. Travelling Waves in Reaction Diffusion Systems with Weak Diffusion: Analytical Techniques and Results.- 14. Spatial Pattern Formation with Reaction/Population Interaction Diffusion Mechanisms.- 15. Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms.- 16. Neural Models of Pattern Formation.- 17. Mechanical Models for Generating Pattern and Form in Development.- 18. Evolution and Developmental Programmes.- 19. Epidemic Models and the Dynamics of Infectious Diseases.- 20. Geographic Spread of Epidemics.- Appendices.- 1. Phase Plane Analysis.- 2. Routh-Hurwitz Conditions, Jury Conditions, Descarte's Rule of Signs and Exact Solutions of a Cubic.- 3. Hopf Bifurcation Theorem and Limit Cycles.- 4. General Results for the Laplacian Operator in Bounded Domains.
