skip to content
Matrices and graphs : stability problems in mathematical ecology Preview this item
ClosePreview this item
Checking...

Matrices and graphs : stability problems in mathematical ecology

Author: D O Logofet
Publisher: Boca Raton : CRC Press, ©1993.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

A survey of applications of mathematical results pertinent to issues of theoretical and applied ecology. The book covers achievements in the field using concepts from matrix theory and graph theory.

Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Additional Physical Format: Online version:
Logofet, Dmitriĭ Olegovich.
Matrices and graphs.
Boca Raton : CRC Press, ©1993
(OCoLC)645897518
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: D O Logofet
ISBN: 0849342465 9780849342462
OCLC Number: 26052515
Description: xi, 308 pages : illustrations ; 24 cm
Contents: 1. Stability Concepts in Ecology and Mathematics --
I. Basic Approaches to the Notion of Stability --
A. Species Diversity as a Measure of Stability --
B. Model Approach to Definitions of Stability --
II. Lyapunov and "Ecological" Stability in Ecosystem Dynamics --
A. Formal Definitions and Interpretations --
B. A General Method for Simple Models --
III. Matrix Properties as a Key to Stability Analysis --
A. Stability of Linear and Linearized Systems --
B. Indecomposability of a Matrix and Strong Connectedness of Its Associated Graph --
IV. Homage to Lyapunov or Why There Are So Many Stability Problems --
2. Leslie Matrix Model: A Challenge to Linear Algebra --
I. Classical Leslie Model: Constant Schedule of the Life Span --
II. Spectral and Asymptotic Properties of the Leslie Operator --
A. Leslie Operator of Simple Structure --
B. Invariant Polynomials and the Jordan Form --
C. Perron-Frobenius Theorem and Convergence to the Limit Structure --
D. Periodic Behavior and a Measure of Stability --
III. Classification of Stable Solutions in the Leslie Model --
A. Equilibrium Stability --
B. Stability of a General Solutions --
C. Imprimitivity and Cycles --
D. Hypothetical Example --
3. Modifications of the Leslie Model --
I. Tackling Variability by "Constancy" Methods --
A. Deviations from a Constant Life Cycle --
B. Small Modifications and the Perturbation Method --
C. Switching Matrices --
II. Block Structure: Tackling Variability within Age Groups --
A. Age-Status Set-Up and Block Matrices --
B. Factorgraphs and Factor-closure --
C. Basic Arcs and the Criterion of Connectedness --
D. Sufficient Conditions of Indecomposability --
III. Time-Dependent Modifications: Limited Uncertainty in Asymptotic Behavior --
A. Lyapunov Exponents and Exponential Separation --
B. Reducibility to a Strongly Positive System --
C. Stability under Permanently Acting Perturbations --
IV. Density-Dependent Modifications: Nonlinearity vs. Asymptotic Diversity --
A. Linearization at Equilibrium --
B. Leslie's Nonlinear Model: Linearization and Perturbation Findings --
C. Leslie's Nonlinear Model: Direct Analysis Findings --
D. Beddington's Nonlinear Model --
E. Stability of the Total Population --
4. Lotka-Volterra Models of n-Species Communities --
I. A Graph of Species Interactions and the Community Matrix --
II. Lotka-Volterra Models and Ecological Balance Equations --
A. The Hypothesis of "Encounters and Equivalents" --
B. Conservation Principle and Balance Equations --
III. Stability in Lotka-Volterra Community Models --
A. Lyapunov Stability of a Feasible Equilibrium --
B. Volterra Conservative and Dissipative Systems --
C. Dynamical Properties of Conservative Systems --
D. Dynamical Properties of Dissipative Systems --
IV. Stable Matrices and Globally Stable Equilibria: What Lies in Between? --
A. D-stability of Matrices --
B. Totally Stable Matrices --
C. From Volterra Dissipative Systems to Dissipative Matrices --
D. Characterizations for 3 X 3 Matrices --
E. Normal Matrices --
V. Self-Limitation Effects versus Species Interactions in Community Stability --
A. Diagonal Dominance and M-Matrices --
B. Stability in Mutualistic Community Models --
C. Diagonally Recessive Matrices --
VI. "Matrix Flower" Growing --
A. Diagram of Logical Relations: Conventions and Examples --
B. Further Relations, or How to Cut the Matrix Flower --
5. Stability Analysis on Community Graphs --
I. Stability in Conservative Systems --
A. Nondirected Graph and Nonsingularity of Its Matrix --
B. Complete Pairing in Trophic Graphs --
II. Qualitative Stability in Model Ecosystems and Sign Stability of the Community Matrix --
A. Qualitative Stability in Model Systems --
B. Equivalence Classes and Sign Stability --
C. Necessary Conditions of Sign Stability --
III. "Color Test" and the Criterion of Sign Stability --
A. Indecomposability and Matrices of O-Symmetry --
B. Predation Graphs and the "Color Test" Failure: Sufficiency --
C. Predation Graphs and the "Color Test" Failure: Necessity --
D. Characterization of Sign-Stable Communities --
IV. Applications: Matrix Theory and Modeling Practice --
A. New Petals in the Matrix Flower --
B. Sign Stability and Multispecies Structures --
C. Case Study: Biocenosis of a Cotton Plant --
D. Case Study: Koshka-Kum Desert Community --
6. Trophic Chains and Stability in Vertical-Structured Communities --
I. Vertical-structured Communities and Trophic Chains --
A. Trophic Chains and the Resource Flow --
B. Trophic Chain of a Finite Length --
II. Equilibria in the Trophic Chain Models --
A. Equilibria in the Open Chain --
B. Equilibria in the Partially Closed Chain --
III. Finite Chain Stability Conditions --
A. Sign Stability in Three-diagonal Matrices --
B. Stability in the Open Chain --
C. Stability in Partially Closed Chains --
D. Finite Chain with the First-Level Closure --
IV. Stability in Generalized Trophic Chain Systems --
V. Practical Examples --
A. Silver Springs Ecosystem --
B. Minimal Territory Estimation for a Top Predator --
7. Ecological Niche Overlap and Stability in Horizontal-Structured Communities --
I. Ecological Niche and the Dynamic Equations for Competitive Species --
A. Resource Spectrum and Utilization Function --
B. Lotka-Volterra Competition Equations --
C. Normal Utilization Functions and the Limits to Similarity --
D. Other Special Cases --
II. Another Representation of Competition Coefficients --
A. Niche Partition as a Metric in the Resource Space --
B. Convex Metrics and Stable Matrices --
III. Positive and Partly Positive Equilibria --
A. When "Partly Positive" Means "Partly Stable" --
B. Geometric Measures of "Equilibriumness" --
C. Whether "Positive" Implies "Partly Positive"? --
IV. Extremal Properties in Horizontal-Structured Community Models --
A. Lotka-Volterra Dynamics as a Steepest Ascent Movement --
B. Towards the Closest Species Packing --
8. Stability in "Box" Models of Spatial Distribution --
I. Can Migration Stabilize a Community? --
A. Migration Flows and United Systems --
B. Migrations in Isotropic Media --
C. Unrealistic Scheme with Real Eigenvalues --
II. Migrations in Anisotropic Media --
A. Migration Exchange between Two Habitats --
B. Prey-Predator Models: Who Migrates after Whom --
C. Migratory Stabilization: Motile Prey --
Sessile Predators --
D. Migratory Stabilization: Sessile Prey --
Motile Predators --
E. When Motility in Common Produces Stability in Equilibria --
III. A Small-Parameter Method to Study Migration Effects --
A. A General Model --
B. Migration Links Shift Feasible Equilibria --
C. Stability and Stabilization --
D. An Example: Asymmetric Exchange between Unequal Habitats.
Responsibility: Dmitrii O. Logofet.
More information:

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/26052515> # Matrices and graphs : stability problems in mathematical ecology
    a schema:Book, schema:CreativeWork ;
   library:oclcnum "26052515" ;
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/flu> ;
   library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/324686163#Place/boca_raton> ; # Boca Raton
   schema:about <http://id.loc.gov/authorities/subjects/sh2008102528> ; # Ecology--Mathematical models
   schema:about <http://id.worldcat.org/fast/901509> ; # Ecology--Mathematical models
   schema:about <http://experiment.worldcat.org/entity/work/data/324686163#Topic/stabilite> ; # Stabilité
   schema:about <http://id.worldcat.org/fast/1012399> ; # Matrices
   schema:about <http://id.worldcat.org/fast/1131203> ; # Stability
   schema:about <http://id.worldcat.org/fast/946584> ; # Graph theory
   schema:about <http://experiment.worldcat.org/entity/work/data/324686163#Topic/biology> ; # Biology
   schema:about <http://dewey.info/class/574.5011/e20/> ;
   schema:about <http://experiment.worldcat.org/entity/work/data/324686163#Topic/graphes_theorie_des> ; # Graphes, Théorie des
   schema:about <http://experiment.worldcat.org/entity/work/data/324686163#Topic/ecologie_modeles_mathematiques> ; # Écologie--Modèles mathématiques
   schema:bookFormat bgn:PrintBook ;
   schema:copyrightYear "1993" ;
   schema:creator <http://viaf.org/viaf/41930118> ; # Dmitriĭ Olegovich Logofet
   schema:datePublished "1993" ;
   schema:description "1. Stability Concepts in Ecology and Mathematics -- I. Basic Approaches to the Notion of Stability -- A. Species Diversity as a Measure of Stability -- B. Model Approach to Definitions of Stability -- II. Lyapunov and "Ecological" Stability in Ecosystem Dynamics -- A. Formal Definitions and Interpretations -- B. A General Method for Simple Models -- III. Matrix Properties as a Key to Stability Analysis -- A. Stability of Linear and Linearized Systems -- B. Indecomposability of a Matrix and Strong Connectedness of Its Associated Graph -- IV. Homage to Lyapunov or Why There Are So Many Stability Problems -- 2. Leslie Matrix Model: A Challenge to Linear Algebra -- I. Classical Leslie Model: Constant Schedule of the Life Span -- II. Spectral and Asymptotic Properties of the Leslie Operator -- A. Leslie Operator of Simple Structure -- B. Invariant Polynomials and the Jordan Form -- C. Perron-Frobenius Theorem and Convergence to the Limit Structure -- D. Periodic Behavior and a Measure of Stability -- III. Classification of Stable Solutions in the Leslie Model -- A. Equilibrium Stability -- B. Stability of a General Solutions -- C. Imprimitivity and Cycles -- D. Hypothetical Example -- 3. Modifications of the Leslie Model -- I. Tackling Variability by "Constancy" Methods -- A. Deviations from a Constant Life Cycle -- B. Small Modifications and the Perturbation Method -- C. Switching Matrices -- II. Block Structure: Tackling Variability within Age Groups -- A. Age-Status Set-Up and Block Matrices -- B. Factorgraphs and Factor-closure -- C. Basic Arcs and the Criterion of Connectedness -- D. Sufficient Conditions of Indecomposability -- III. Time-Dependent Modifications: Limited Uncertainty in Asymptotic Behavior -- A. Lyapunov Exponents and Exponential Separation -- B. Reducibility to a Strongly Positive System -- C. Stability under Permanently Acting Perturbations -- IV. Density-Dependent Modifications: Nonlinearity vs. Asymptotic Diversity -- A. Linearization at Equilibrium -- B. Leslie's Nonlinear Model: Linearization and Perturbation Findings -- C. Leslie's Nonlinear Model: Direct Analysis Findings -- D. Beddington's Nonlinear Model -- E. Stability of the Total Population -- 4. Lotka-Volterra Models of n-Species Communities -- I. A Graph of Species Interactions and the Community Matrix -- II. Lotka-Volterra Models and Ecological Balance Equations -- A. The Hypothesis of "Encounters and Equivalents" -- B. Conservation Principle and Balance Equations -- III. Stability in Lotka-Volterra Community Models -- A. Lyapunov Stability of a Feasible Equilibrium -- B. Volterra Conservative and Dissipative Systems -- C. Dynamical Properties of Conservative Systems -- D. Dynamical Properties of Dissipative Systems -- IV. Stable Matrices and Globally Stable Equilibria: What Lies in Between? -- A. D-stability of Matrices -- B. Totally Stable Matrices -- C. From Volterra Dissipative Systems to Dissipative Matrices -- D. Characterizations for 3 X 3 Matrices -- E. Normal Matrices -- V. Self-Limitation Effects versus Species Interactions in Community Stability -- A. Diagonal Dominance and M-Matrices -- B. Stability in Mutualistic Community Models -- C. Diagonally Recessive Matrices -- VI. "Matrix Flower" Growing -- A. Diagram of Logical Relations: Conventions and Examples -- B. Further Relations, or How to Cut the Matrix Flower -- 5. Stability Analysis on Community Graphs -- I. Stability in Conservative Systems -- A. Nondirected Graph and Nonsingularity of Its Matrix -- B. Complete Pairing in Trophic Graphs -- II. Qualitative Stability in Model Ecosystems and Sign Stability of the Community Matrix -- A. Qualitative Stability in Model Systems -- B. Equivalence Classes and Sign Stability -- C. Necessary Conditions of Sign Stability -- III. "Color Test" and the Criterion of Sign Stability -- A. Indecomposability and Matrices of O-Symmetry -- B. Predation Graphs and the "Color Test" Failure: Sufficiency -- C. Predation Graphs and the "Color Test" Failure: Necessity -- D. Characterization of Sign-Stable Communities -- IV. Applications: Matrix Theory and Modeling Practice -- A. New Petals in the Matrix Flower -- B. Sign Stability and Multispecies Structures -- C. Case Study: Biocenosis of a Cotton Plant -- D. Case Study: Koshka-Kum Desert Community -- 6. Trophic Chains and Stability in Vertical-Structured Communities -- I. Vertical-structured Communities and Trophic Chains -- A. Trophic Chains and the Resource Flow -- B. Trophic Chain of a Finite Length -- II. Equilibria in the Trophic Chain Models -- A. Equilibria in the Open Chain -- B. Equilibria in the Partially Closed Chain -- III. Finite Chain Stability Conditions -- A. Sign Stability in Three-diagonal Matrices -- B. Stability in the Open Chain -- C. Stability in Partially Closed Chains -- D. Finite Chain with the First-Level Closure -- IV. Stability in Generalized Trophic Chain Systems -- V. Practical Examples -- A. Silver Springs Ecosystem -- B. Minimal Territory Estimation for a Top Predator -- 7. Ecological Niche Overlap and Stability in Horizontal-Structured Communities -- I. Ecological Niche and the Dynamic Equations for Competitive Species -- A. Resource Spectrum and Utilization Function -- B. Lotka-Volterra Competition Equations -- C. Normal Utilization Functions and the Limits to Similarity -- D. Other Special Cases -- II. Another Representation of Competition Coefficients -- A. Niche Partition as a Metric in the Resource Space -- B. Convex Metrics and Stable Matrices -- III. Positive and Partly Positive Equilibria -- A. When "Partly Positive" Means "Partly Stable" -- B. Geometric Measures of "Equilibriumness" -- C. Whether "Positive" Implies "Partly Positive"? -- IV. Extremal Properties in Horizontal-Structured Community Models -- A. Lotka-Volterra Dynamics as a Steepest Ascent Movement -- B. Towards the Closest Species Packing -- 8. Stability in "Box" Models of Spatial Distribution -- I. Can Migration Stabilize a Community? -- A. Migration Flows and United Systems -- B. Migrations in Isotropic Media -- C. Unrealistic Scheme with Real Eigenvalues -- II. Migrations in Anisotropic Media -- A. Migration Exchange between Two Habitats -- B. Prey-Predator Models: Who Migrates after Whom -- C. Migratory Stabilization: Motile Prey -- Sessile Predators -- D. Migratory Stabilization: Sessile Prey -- Motile Predators -- E. When Motility in Common Produces Stability in Equilibria -- III. A Small-Parameter Method to Study Migration Effects -- A. A General Model -- B. Migration Links Shift Feasible Equilibria -- C. Stability and Stabilization -- D. An Example: Asymmetric Exchange between Unequal Habitats."@en ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/324686163> ;
   schema:inLanguage "en" ;
   schema:isSimilarTo <http://www.worldcat.org/oclc/645897518> ;
   schema:name "Matrices and graphs : stability problems in mathematical ecology"@en ;
   schema:productID "26052515" ;
   schema:publication <http://www.worldcat.org/title/-/oclc/26052515#PublicationEvent/boca_raton_crc_press_1993> ;
   schema:publisher <http://experiment.worldcat.org/entity/work/data/324686163#Agent/crc_press> ; # CRC Press
   schema:url <http://www.gbv.de/dms/bowker/toc/9780849342462.pdf> ;
   schema:workExample <http://worldcat.org/isbn/9780849342462> ;
   umbel:isLike <http://bnb.data.bl.uk/id/resource/GB93Z1938> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/26052515> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/324686163#Topic/ecologie_modeles_mathematiques> # Écologie--Modèles mathématiques
    a schema:Intangible ;
   schema:name "Écologie--Modèles mathématiques"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/324686163#Topic/graphes_theorie_des> # Graphes, Théorie des
    a schema:Intangible ;
   schema:name "Graphes, Théorie des"@en ;
    .

<http://id.loc.gov/authorities/subjects/sh2008102528> # Ecology--Mathematical models
    a schema:Intangible ;
   schema:name "Ecology--Mathematical models"@en ;
    .

<http://id.worldcat.org/fast/1012399> # Matrices
    a schema:Intangible ;
   schema:name "Matrices"@en ;
    .

<http://id.worldcat.org/fast/1131203> # Stability
    a schema:Intangible ;
   schema:name "Stability"@en ;
    .

<http://id.worldcat.org/fast/901509> # Ecology--Mathematical models
    a schema:Intangible ;
   schema:name "Ecology--Mathematical models"@en ;
    .

<http://id.worldcat.org/fast/946584> # Graph theory
    a schema:Intangible ;
   schema:name "Graph theory"@en ;
    .

<http://viaf.org/viaf/41930118> # Dmitriĭ Olegovich Logofet
    a schema:Person ;
   schema:familyName "Logofet" ;
   schema:givenName "Dmitriĭ Olegovich" ;
   schema:givenName "D. O." ;
   schema:name "Dmitriĭ Olegovich Logofet" ;
    .

<http://worldcat.org/isbn/9780849342462>
    a schema:ProductModel ;
   schema:isbn "0849342465" ;
   schema:isbn "9780849342462" ;
    .

<http://www.worldcat.org/oclc/645897518>
    a schema:CreativeWork ;
   rdfs:label "Matrices and graphs." ;
   schema:description "Online version:" ;
   schema:isSimilarTo <http://www.worldcat.org/oclc/26052515> ; # Matrices and graphs : stability problems in mathematical ecology
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.