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Spatial ecology via reaction-diffusion equations [[electronic resource] /] / Robert Stephen Cantrell and Chris Cosner
| Spatial ecology via reaction-diffusion equations [[electronic resource] /] / Robert Stephen Cantrell and Chris Cosner |
| Autore | Cantrell Robert Stephen |
| Pubbl/distr/stampa | Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2003 |
| Descrizione fisica | 1 online resource (429 p.) |
| Disciplina | 577.01515353 |
| Altri autori (Persone) | CosnerChris |
| Collana | Wiley series in mathematical and computational biology |
| Soggetto topico |
Spatial ecology - Mathematical models
Reaction-diffusion equations |
| ISBN |
1-280-27395-X
9786610273959 0-470-32237-3 0-470-87128-8 0-470-87129-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Spatial Ecology via Reaction-Diffusion Equations; Contents; Preface; Series Preface; 1 Introduction; 1.1 Introductory Remarks; 1.2 Nonspatial Models for a Single Species; 1.3 Nonspatial Models For Interacting Species; 1.3.1 Mass-Action and Lotka-Volterra Models; 1.3.2 Beyond Mass-Action: The Functional Response; 1.4 Spatial Models: A General Overview; 1.5 Reaction-Diffusion Models; 1.5.1 Deriving Diffusion Models; 1.5.2 Diffusion Models Via Interacting Particle Systems: The Importance of Being Smooth; 1.5.3 What Can Reaction-Diffusion Models Tell Us?
1.5.4 Edges, Boundary Conditions, and Environmental Heterogeneity1.6 Mathematical Background; 1.6.1 Dynamical Systems; 1.6.2 Basic Concepts in Partial Differential Equations: An Example; 1.6.3 Modern Approaches to Partial Differential Equations: Analogies with Linear Algebra and Matrix Theory; 1.6.4 Elliptic Operators: Weak Solutions, State Spaces, and Mapping Properties; 1.6.5 Reaction-Diffusion Models as Dynamical Systems; 1.6.6 Classical Regularity Theory for Parabolic Equations; 1.6.7 Maximum Principles and Monotonicity 2 Linear Growth Models for a Single Species: Averaging Spatial Effects Via Eigenvalues2.1 Eigenvalues, Persistence, and Scaling in Simple Models; 2.1.1 An Application: Species-Area Relations; 2.2 Variational Formulations of Eigenvalues: Accounting for Heterogeneity; 2.3 Effects of Fragmentation and Advection/Taxis in Simple Linear Models; 2.3.1 Fragmentation; 2.3.2 Advection/Taxis; 2.4 Graphical Analysis in One Space Dimension; 2.4.1 The Best Location for a Favorable Habitat Patch; 2.4.2 Effects of Buffer Zones and Boundary Behavior; 2.5 Eigenvalues and Positivity; 2.5.1 Advective Models 2.5.2 Time Periodicity2.5.3 Additional Results on Eigenvalues and Positivity; 2.6 Connections with Other Topics and Models; 2.6.1 Eigenvalues, Solvability, and Multiplicity; 2.6.2 Other Model Types: Discrete Space and Time; 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; 3.2.1 Persistence and Extinction; 3.2.2 Minimal Patch Sizes; 3.2.3 Uniqueness of Equilibria; 3.3 Equilibria and Scaling: One Space Dimension; 3.3.1 Minimum Patch Size Revisited 3.4 Continuation and Bifurcation of Equilibria3.4.1 Continuation; 3.4.2 Bifurcation Results; 3.4.3 Discussion and Conclusions; 3.5 Applications and Properties of Single Species Models; 3.5.1 How Predator Incursions Affect Critical Patch Size; 3.5.2 Diffusion and Allee Effects; 3.5.3 Properties of Equilibria; 3.6 More General Single Species Models; Appendix; 4 Permanence; 4.1 Introduction; 4.1.1 Ecological Overview; 4.1.2 ODE Models as Examples; 4.1.3 A Little Historical Perspective; 4.2 Definition of Permanence; 4.2.1 Ecological Permanence; 4.2.2 Abstract Permanence 4.3 Techniques for Establishing Permanence |
| Record Nr. | UNINA-9910143511803321 |
Cantrell Robert Stephen
|
||
| Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Spatial ecology via reaction-diffusion equations [[electronic resource] /] / Robert Stephen Cantrell and Chris Cosner
| Spatial ecology via reaction-diffusion equations [[electronic resource] /] / Robert Stephen Cantrell and Chris Cosner |
| Autore | Cantrell Robert Stephen |
| Pubbl/distr/stampa | Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2003 |
| Descrizione fisica | 1 online resource (429 p.) |
| Disciplina | 577.01515353 |
| Altri autori (Persone) | CosnerChris |
| Collana | Wiley series in mathematical and computational biology |
| Soggetto topico |
Spatial ecology - Mathematical models
Reaction-diffusion equations |
| ISBN |
1-280-27395-X
9786610273959 0-470-32237-3 0-470-87128-8 0-470-87129-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Spatial Ecology via Reaction-Diffusion Equations; Contents; Preface; Series Preface; 1 Introduction; 1.1 Introductory Remarks; 1.2 Nonspatial Models for a Single Species; 1.3 Nonspatial Models For Interacting Species; 1.3.1 Mass-Action and Lotka-Volterra Models; 1.3.2 Beyond Mass-Action: The Functional Response; 1.4 Spatial Models: A General Overview; 1.5 Reaction-Diffusion Models; 1.5.1 Deriving Diffusion Models; 1.5.2 Diffusion Models Via Interacting Particle Systems: The Importance of Being Smooth; 1.5.3 What Can Reaction-Diffusion Models Tell Us?
1.5.4 Edges, Boundary Conditions, and Environmental Heterogeneity1.6 Mathematical Background; 1.6.1 Dynamical Systems; 1.6.2 Basic Concepts in Partial Differential Equations: An Example; 1.6.3 Modern Approaches to Partial Differential Equations: Analogies with Linear Algebra and Matrix Theory; 1.6.4 Elliptic Operators: Weak Solutions, State Spaces, and Mapping Properties; 1.6.5 Reaction-Diffusion Models as Dynamical Systems; 1.6.6 Classical Regularity Theory for Parabolic Equations; 1.6.7 Maximum Principles and Monotonicity 2 Linear Growth Models for a Single Species: Averaging Spatial Effects Via Eigenvalues2.1 Eigenvalues, Persistence, and Scaling in Simple Models; 2.1.1 An Application: Species-Area Relations; 2.2 Variational Formulations of Eigenvalues: Accounting for Heterogeneity; 2.3 Effects of Fragmentation and Advection/Taxis in Simple Linear Models; 2.3.1 Fragmentation; 2.3.2 Advection/Taxis; 2.4 Graphical Analysis in One Space Dimension; 2.4.1 The Best Location for a Favorable Habitat Patch; 2.4.2 Effects of Buffer Zones and Boundary Behavior; 2.5 Eigenvalues and Positivity; 2.5.1 Advective Models 2.5.2 Time Periodicity2.5.3 Additional Results on Eigenvalues and Positivity; 2.6 Connections with Other Topics and Models; 2.6.1 Eigenvalues, Solvability, and Multiplicity; 2.6.2 Other Model Types: Discrete Space and Time; 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; 3.2.1 Persistence and Extinction; 3.2.2 Minimal Patch Sizes; 3.2.3 Uniqueness of Equilibria; 3.3 Equilibria and Scaling: One Space Dimension; 3.3.1 Minimum Patch Size Revisited 3.4 Continuation and Bifurcation of Equilibria3.4.1 Continuation; 3.4.2 Bifurcation Results; 3.4.3 Discussion and Conclusions; 3.5 Applications and Properties of Single Species Models; 3.5.1 How Predator Incursions Affect Critical Patch Size; 3.5.2 Diffusion and Allee Effects; 3.5.3 Properties of Equilibria; 3.6 More General Single Species Models; Appendix; 4 Permanence; 4.1 Introduction; 4.1.1 Ecological Overview; 4.1.2 ODE Models as Examples; 4.1.3 A Little Historical Perspective; 4.2 Definition of Permanence; 4.2.1 Ecological Permanence; 4.2.2 Abstract Permanence 4.3 Techniques for Establishing Permanence |
| Record Nr. | UNINA-9910830560903321 |
|
Cantrell Robert Stephen
|
||
| Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Spatial ecology via reaction-diffusion equations / / Robert Stephen Cantrell and Chris Cosner
| Spatial ecology via reaction-diffusion equations / / Robert Stephen Cantrell and Chris Cosner |
| Autore | Cantrell Robert Stephen |
| Pubbl/distr/stampa | Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2003 |
| Descrizione fisica | 1 online resource (429 p.) |
| Disciplina | 577/.015/1 |
| Altri autori (Persone) | CosnerChris |
| Collana | Wiley series in mathematical and computational biology |
| Soggetto topico |
Spatial ecology - Mathematical models
Reaction-diffusion equations |
| ISBN |
1-280-27395-X
9786610273959 0-470-32237-3 0-470-87128-8 0-470-87129-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Spatial Ecology via Reaction-Diffusion Equations; Contents; Preface; Series Preface; 1 Introduction; 1.1 Introductory Remarks; 1.2 Nonspatial Models for a Single Species; 1.3 Nonspatial Models For Interacting Species; 1.3.1 Mass-Action and Lotka-Volterra Models; 1.3.2 Beyond Mass-Action: The Functional Response; 1.4 Spatial Models: A General Overview; 1.5 Reaction-Diffusion Models; 1.5.1 Deriving Diffusion Models; 1.5.2 Diffusion Models Via Interacting Particle Systems: The Importance of Being Smooth; 1.5.3 What Can Reaction-Diffusion Models Tell Us?
1.5.4 Edges, Boundary Conditions, and Environmental Heterogeneity1.6 Mathematical Background; 1.6.1 Dynamical Systems; 1.6.2 Basic Concepts in Partial Differential Equations: An Example; 1.6.3 Modern Approaches to Partial Differential Equations: Analogies with Linear Algebra and Matrix Theory; 1.6.4 Elliptic Operators: Weak Solutions, State Spaces, and Mapping Properties; 1.6.5 Reaction-Diffusion Models as Dynamical Systems; 1.6.6 Classical Regularity Theory for Parabolic Equations; 1.6.7 Maximum Principles and Monotonicity 2 Linear Growth Models for a Single Species: Averaging Spatial Effects Via Eigenvalues2.1 Eigenvalues, Persistence, and Scaling in Simple Models; 2.1.1 An Application: Species-Area Relations; 2.2 Variational Formulations of Eigenvalues: Accounting for Heterogeneity; 2.3 Effects of Fragmentation and Advection/Taxis in Simple Linear Models; 2.3.1 Fragmentation; 2.3.2 Advection/Taxis; 2.4 Graphical Analysis in One Space Dimension; 2.4.1 The Best Location for a Favorable Habitat Patch; 2.4.2 Effects of Buffer Zones and Boundary Behavior; 2.5 Eigenvalues and Positivity; 2.5.1 Advective Models 2.5.2 Time Periodicity2.5.3 Additional Results on Eigenvalues and Positivity; 2.6 Connections with Other Topics and Models; 2.6.1 Eigenvalues, Solvability, and Multiplicity; 2.6.2 Other Model Types: Discrete Space and Time; 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; 3.2.1 Persistence and Extinction; 3.2.2 Minimal Patch Sizes; 3.2.3 Uniqueness of Equilibria; 3.3 Equilibria and Scaling: One Space Dimension; 3.3.1 Minimum Patch Size Revisited 3.4 Continuation and Bifurcation of Equilibria3.4.1 Continuation; 3.4.2 Bifurcation Results; 3.4.3 Discussion and Conclusions; 3.5 Applications and Properties of Single Species Models; 3.5.1 How Predator Incursions Affect Critical Patch Size; 3.5.2 Diffusion and Allee Effects; 3.5.3 Properties of Equilibria; 3.6 More General Single Species Models; Appendix; 4 Permanence; 4.1 Introduction; 4.1.1 Ecological Overview; 4.1.2 ODE Models as Examples; 4.1.3 A Little Historical Perspective; 4.2 Definition of Permanence; 4.2.1 Ecological Permanence; 4.2.2 Abstract Permanence 4.3 Techniques for Establishing Permanence |
| Record Nr. | UNINA-9910877380203321 |
|
Cantrell Robert Stephen
|
||
| Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||