Stephen Cantrell, Christopher Cosner

Spatial Ecology Via Reaction-Diffusion Equations

• Gebundenes Buch

Produktbeschreibung

Viele Probleme aus der Ökologie, darunter zum Beispiel die Ausbreitung von Schadstoffen, lassen sich modellieren, wenn man auf scheinbar zufällige Prozesse mit einer räumlichen und gegebenenfalls auch einer zeitlichen Dimension zurückgreift. Dieses Buch zeigt Ihnen, wie man räumliche Effekte in der Ökologie und Populationsdynamik mit so genannten Reaktions-Diffusions-Modellen beschreiben kann. Sie lernen, Modelle aufzubauen und die Resultate zu interpretieren. Die Umsetzung der Theorie in die Praxis wird anhand spezieller Anwendungsbeispiele demonstriert.

Produktdetails

• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 432
• Erscheinungstermin: 1. Oktober 2003
• Englisch
• Abmessung: 260mm x 183mm x 27mm
• Gewicht: 945g
• ISBN-13: 9780471493013
• ISBN-10: 0471493015
• Artikelnr.: 10239271

Autorenporträt

Robert Stephen Cantrell is the author of Spatial Ecology via Reaction-Diffusion Equations, published by Wiley. Chris Cosner is the author of Spatial Ecology via Reaction-Diffusion Equations, published by Wiley.

Inhaltsangabe

Preface.
Series Preface.
1 Introduction.
1.1 Introductory Remarks.
1.2 Nonspatial Models for a Single Species.
1.3 Nonspatial Models For Interacting Species.
1.4 Spatial Models: A General Overview.
1.5 Reaction-Diffusion Models.
1.6 Mathematical Background.
2 Linear Growth Models for a Single Species: Averaging Spatial Effects Via
Eigenvalues.
2.1 Eigenvalues, Persistence, and Scaling in Simple Models.
2.2 Variational Formulations of Eigenvalues: Accounting for Heterogeneity.
2.3 Effects of Fragmentation and Advection/Taxis in Simple Linear Models.
2.4 Graphical Analysis in One Space Dimension.
2.5 Eigenvalues and Positivity.
2.6 Connections with Other Topics and Models.
Appendix.
3 Density Dependent Single-Species Models.
3.1 The Importance of Equilibria in Single Species Models.
3.2 Equilibria and Stability: Sub- and Supersolutions.
3.3 Equilibria and Scaling: One Space Dimension.
3.4 Continuation and Bifurcation of Equilibria.
3.5 Applications and Properties of Single Species Models.
3.6 More General Single Species Models.
Appendix.
4 Permanence.
4.1 Introduction.
4.2 Definition of Permanence.
4.3 Techniques for Establishing Permanence.
4.4 Invasibility Implies Coexistence.
4.5 Permanence in Reaction-Diffusion Models for Predation.
4.6 Ecological Permanence and Equilibria.
Appendix.
5 Beyond Permanence: More Persistence Theory.
5.1 Introduction.
5.2 Compressivity.
5.3 Practical Persistence.
5.4 Bounding Transient Orbits.
5.5 Persistence in Nonautonomous Systems.
5.6 Conditional Persistence.
5.7 Extinction Results.
Appendix.
6 Spatial Heterogeneity in Reaction-Diffusion Models.
6.1 Introduction.
6.2 Spatial Heterogeneity within the Habitat Patch.
6.3 Edge Mediated Effects.
6.4 Estimates and Consequences.
Appendix.
7 Nonmonotone Systems.
7.1 Introduction.
7.2 Predator Mediated Coexistence.
7.3 Three Species Competition.
7.4 Three Trophic Level Models.
Appendix.
References.
Index.

Rezensionen

"...particularly attractive and useful for graduate students and other researchers who are interested in studying applications of reaction-diffusion theory to spatial ecology." ( Mathematical Reviews , Issue 2007a)
"...I would recommend this book to anyone who wants a well supported journey into the modern theory of partial differential equations and dynamic systems..." ( The Mathematical Gazette , March 2005)