Format:
Online-Ressource
ISBN:
9783642110696
Series Statement:
C.I.M.E. Summer Schools 80
Content:
This title includes: K.L. Cooke: Delay differential equations; J.M. Cushing: Volterra integrodifferential equations in population dynamics; K.P. Hadeler: Diffusion equations in biology; S. Hastings: Some mathematical problems arising in neurobiology; F.C. Hoppensteadt: Perturbation methods in biology; and, S.O. Londen: Integral equations of Volterra type
Note:
Description based upon print version of record
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Mathematics of Biology; Copyright Page; Contents; Delay Differential Equations; 1. Introduction; Chapter I. Basic Concepts; Chapter II. Autonomous Linear Functional Differential Equations; Chapter III. Stability Conditions for Exponential Polynomials and Entire Functions; References; Volterra Integrodifferential Equations in Population Dynamics; Introduction; Chapter 1. Some Models for Population Growth; Chapter 2. Stability and Single Species Models; Chapter 3. Single Species Osciliations in a Constant Environment; Chapter 4. Single Species Oscillations in a Periodic Environment
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Chapter 5. Predator-Prey Interactions and Response DelaysChapter 6. Two Species Competition; Appendix A; Appendix B; Appendix C; References; Diffusion Equations in Biology; 1. Morphogenesis models and pattern formation; 2. Stable matrices; 3. Destabilizing boundary conditions; 4. The concept of invariant sets for parabolic equations; 5. Nonlinear Dirichlet problems; 6. The "Brusselator"; 7. The Gierer-Meinhardt-Model; 8. Maginu's morphoqenesis model; 9. The Classical competition model; 10. The Lotka-Volterra model; 11. The Fisher-Wright-Haldane modle of population qenetics
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12. The population qenetic model for m alleles13. Traveling fronts and pulses; 14. Branching processes with diffusion; References; Some Mathematical Problems Arising in Neurobiology; Introduction; I. Physiological Background, Work of Hodgkin and Huxley, Hodgkin-Huxley Equations; II. Mathematical Problems for the Hodgkin-Huxley Equations; Simplified Models; III. Existence Proofs for Travelling Waves; IV. Stability, Multiple Pulses, Spatially Homogenous Solutions; V. Mult-cellular Phenomena, Relation to Chemical Patterns; VI. Discrete Models of Excitable Madia; Perturbation Methods in Biology
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I. Introduction to Human GeneticsII. Random Models; III. A Nonlimear Renewal Bquation With Periodic and Chaotic Solutions; IV. Respiration Control; V. Computer Studies of Nonlinear Oscillators; Bibliography; Primary Sources; Integral Equations of Volterra Type; 0. Introduction; 1. Existence, Uniqueness and Continuity of Solutions; 2. Resolvent Theory; 3. Limit Equations; 4. Boundeness of Solutions; 5. Spectral Results, Linear Case; 6. Spectral and Asymptotic Results, Nonlinear Case; 7. Abstract Equations; References;
Language:
English
Keywords:
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