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Mathematics of Biology.

Author: Mimmo Iannelli
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
Series: C.I.M.E. Summer Schools, 80.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Mimmo Iannelli
ISBN: 3642110681 9783642110689 9783642110696 364211069X
OCLC Number: 990534377
Language Note: English.
Notes: III. A Nonlimear Renewal Bquation With Periodic and Chaotic Solutions.
Description: 1 online resource (360 pages).
Contents: Mathematics of Biology; Copyright Page; Contents; Delay Differential Equations; 1. Introduction; Chapter I. Basic Concepts; 2. Sources of delay differential equations in biology; 3. The class of equations considered; 4. The initial value problem; 5. Operator of translation along trajectories; 6. Equations with unbounded delay; Chapter II. Autonomous Linear Functional Differential Equations; 7. Linear autonomous systems and semigroups; 8. The Laplace transform and explicit representations; 9. Stability by linearization. Chapter III. Stability Conditions for Exponential Polynomials and Entire Functions10. Criteria for stability; 11. Liapunov functionals; 12. Construction of Liapunov functions for linear delay equations; 13. Method of ejective fixed points; 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. 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. 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; References for Lecture I; II. Mathematical Problems for the Hodgkin-Huxley Equations; Simplified Models; 1. Existence and Uniqueness of Solutions; 2. Existence of Travelling Waves; 3. Local Stability of Travelling Waves; 4. Global Stability, Thresholds, Interaction of Waves; 5. Semi-infinite and Finite Axons.
Series Title: C.I.M.E. Summer Schools, 80.
Other Titles: C.I.M.E. Summer Schools, 80
C.I.M.E. Summer Schools, Volume 80

Abstract:

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.

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