Lotka-Volterra and Related Systems :: Recent Developments in Population Dynamics.
This book facilitates research in the general area of population dynamics by presenting some of the recent developments involving theories, methods and application in this important area of research. The underlying common feature of the studies included in the book is that they are related, either d...
Gespeichert in:
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| Weitere Verfasser: | , , , , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin :
De Gruyter,
2013.
|
| Schriftenreihe: | De Gruyter series in mathematics and life sciences.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book facilitates research in the general area of population dynamics by presenting some of the recent developments involving theories, methods and application in this important area of research. The underlying common feature of the studies included in the book is that they are related, either directly or indirectly, to the well-known Lotka-Volterra systems which offer a variety of mathematical concepts from both theoretical and application points of view. |
| Beschreibung: | 1 online resource (244 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9783110269840 3110269848 3110269511 9783110269512 |
Internformat
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| 505 | 0 | |a Preface; Permanence, global attraction and stability; 1 Introduction; 2 Existence of a compact uniform attractor; 3 Proof of Theorems 2.1, 2.2 and 2.3; 4 Partial permanence and permanence; 5 Necessary conditions for permanence of Lotka-Volterra systems; 6 Sufficient condition for permanence of Lotka-Volterra systems; 7 Further notes; 8 Global attraction and stability of Lotka-Volterra systems; 9 Global stability by Lyapunov functions; 10 Global stability by split Lyapunov functions; 10.1 Checking the conditions (10.2) and (10.8); 10.2 Examples. | |
| 505 | 8 | |a 11 Global stability of competitive Lotka-Volterra systems12 Global attraction of competitive Lotka-Volterra systems; 13 Some notes; Bibliography; Competitive Lotka-Volterra systems with periodic coefficients; 1 Introduction; 2 The autonomous model. The logistic equation; 3 Two species periodic models; 4 Competitive exclusion; 5 One species extinction in three-dimensional models; 6 The impulsive logistic equation; 7 Two species systems with impulsive effects. A look at the N-dimensional case; 8 The influence of impulsive perturbations on extinction in three-species models; Bibliography. | |
| 505 | 8 | |a Fixed points, periodic points and chaotic dynamics for continuous maps with applications to population dynamics1 Introduction; 2 Notation; 3 Search of fixed points for maps expansive along one direction; 4 The planar case; 4.1 Stretching along the paths and variants; 4.2 The Crossing Lemma; 5 The N-dimensional setting: Intersection Lemma; 5.1 Zero-sets of maps depending on parameters; 5.2 Stretching along the paths in the N-dimensional case; 6 Chaotic dynamics for continuous maps; 7 Definitions and main results; 8 Symbolic dynamics; 9 On various notions of chaos; 10 Linked twist maps. | |
| 505 | 8 | |a 11 Examples from the ODEs12 Predator-prey model; 12.1 The effects of a periodic harvesting; 12.2 Technical details and proofs; Bibliography; Index. | |
| 520 | |a This book facilitates research in the general area of population dynamics by presenting some of the recent developments involving theories, methods and application in this important area of research. The underlying common feature of the studies included in the book is that they are related, either directly or indirectly, to the well-known Lotka-Volterra systems which offer a variety of mathematical concepts from both theoretical and application points of view. | ||
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references and index. | ||
| 650 | 0 | |a Lotka-Volterra equations. |0 http://id.loc.gov/authorities/subjects/sh2011003271 | |
| 650 | 0 | |a Population biology |x Mathematical models. | |
| 650 | 6 | |a Biologie des populations |x Modèles mathématiques. | |
| 650 | 7 | |a NATURE |x Ecology. |2 bisacsh | |
| 650 | 7 | |a NATURE |x Ecosystems & Habitats |x Wilderness. |2 bisacsh | |
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| 650 | 7 | |a Kolmogorovsche Differentialgleichungen |2 gnd |0 http://d-nb.info/gnd/4164698-8 | |
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| 650 | 7 | |a Populationsdynamik |2 gnd |0 http://d-nb.info/gnd/4046803-3 | |
| 653 | |a Lotka-Volterra System. | ||
| 653 | |a Population Dynamics. | ||
| 700 | 1 | |a Lisena, Benedetta. | |
| 700 | 1 | |a Pireddu, Marina. | |
| 700 | 1 | |a Zanolin, Fabio. | |
| 700 | 1 | |a Ahmad, Shair. |0 http://id.loc.gov/authorities/names/n80048820 | |
| 700 | 1 | |a Stamova, Ivanka. |0 http://id.loc.gov/authorities/names/no2010079775 | |
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| _version_ | 1816882237493215232 |
| adam_text | |
| any_adam_object | |
| author | Hou, Zhanyuan |
| author2 | Lisena, Benedetta Pireddu, Marina Zanolin, Fabio Ahmad, Shair Stamova, Ivanka |
| author2_role | |
| author2_variant | b l bl m p mp f z fz s a sa i s is |
| author_GND | http://id.loc.gov/authorities/names/nr91016611 http://id.loc.gov/authorities/names/n80048820 http://id.loc.gov/authorities/names/no2010079775 |
| author_facet | Hou, Zhanyuan Lisena, Benedetta Pireddu, Marina Zanolin, Fabio Ahmad, Shair Stamova, Ivanka |
| author_role | |
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| author_variant | z h zh |
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| callnumber-first | Q - Science |
| callnumber-label | QH352 |
| callnumber-raw | QH352 .L67 2013 |
| callnumber-search | QH352 .L67 2013 |
| callnumber-sort | QH 3352 L67 42013 |
| callnumber-subject | QH - Natural History and Biology |
| classification_rvk | SK 520 |
| collection | ZDB-4-EBA |
| contents | Preface; Permanence, global attraction and stability; 1 Introduction; 2 Existence of a compact uniform attractor; 3 Proof of Theorems 2.1, 2.2 and 2.3; 4 Partial permanence and permanence; 5 Necessary conditions for permanence of Lotka-Volterra systems; 6 Sufficient condition for permanence of Lotka-Volterra systems; 7 Further notes; 8 Global attraction and stability of Lotka-Volterra systems; 9 Global stability by Lyapunov functions; 10 Global stability by split Lyapunov functions; 10.1 Checking the conditions (10.2) and (10.8); 10.2 Examples. 11 Global stability of competitive Lotka-Volterra systems12 Global attraction of competitive Lotka-Volterra systems; 13 Some notes; Bibliography; Competitive Lotka-Volterra systems with periodic coefficients; 1 Introduction; 2 The autonomous model. The logistic equation; 3 Two species periodic models; 4 Competitive exclusion; 5 One species extinction in three-dimensional models; 6 The impulsive logistic equation; 7 Two species systems with impulsive effects. A look at the N-dimensional case; 8 The influence of impulsive perturbations on extinction in three-species models; Bibliography. Fixed points, periodic points and chaotic dynamics for continuous maps with applications to population dynamics1 Introduction; 2 Notation; 3 Search of fixed points for maps expansive along one direction; 4 The planar case; 4.1 Stretching along the paths and variants; 4.2 The Crossing Lemma; 5 The N-dimensional setting: Intersection Lemma; 5.1 Zero-sets of maps depending on parameters; 5.2 Stretching along the paths in the N-dimensional case; 6 Chaotic dynamics for continuous maps; 7 Definitions and main results; 8 Symbolic dynamics; 9 On various notions of chaos; 10 Linked twist maps. 11 Examples from the ODEs12 Predator-prey model; 12.1 The effects of a periodic harvesting; 12.2 Technical details and proofs; Bibliography; Index. |
| ctrlnum | (OCoLC)851970552 |
| dewey-full | 577.8/8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 577 - Ecology |
| dewey-raw | 577.8/8 |
| dewey-search | 577.8/8 |
| dewey-sort | 3577.8 18 |
| dewey-tens | 570 - Biology |
| discipline | Biologie Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn851970552 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:25Z |
| institution | BVB |
| isbn | 9783110269840 3110269848 3110269511 9783110269512 |
| language | English |
| oclc_num | 851970552 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (244 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | De Gruyter, |
| record_format | marc |
| series | De Gruyter series in mathematics and life sciences. |
| series2 | De Gruyter Series in Mathematics and Life Sciences |
| spelling | Hou, Zhanyuan. http://id.loc.gov/authorities/names/nr91016611 Lotka-Volterra and Related Systems : Recent Developments in Population Dynamics. Berlin : De Gruyter, 2013. 1 online resource (244 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter Series in Mathematics and Life Sciences Preface; Permanence, global attraction and stability; 1 Introduction; 2 Existence of a compact uniform attractor; 3 Proof of Theorems 2.1, 2.2 and 2.3; 4 Partial permanence and permanence; 5 Necessary conditions for permanence of Lotka-Volterra systems; 6 Sufficient condition for permanence of Lotka-Volterra systems; 7 Further notes; 8 Global attraction and stability of Lotka-Volterra systems; 9 Global stability by Lyapunov functions; 10 Global stability by split Lyapunov functions; 10.1 Checking the conditions (10.2) and (10.8); 10.2 Examples. 11 Global stability of competitive Lotka-Volterra systems12 Global attraction of competitive Lotka-Volterra systems; 13 Some notes; Bibliography; Competitive Lotka-Volterra systems with periodic coefficients; 1 Introduction; 2 The autonomous model. The logistic equation; 3 Two species periodic models; 4 Competitive exclusion; 5 One species extinction in three-dimensional models; 6 The impulsive logistic equation; 7 Two species systems with impulsive effects. A look at the N-dimensional case; 8 The influence of impulsive perturbations on extinction in three-species models; Bibliography. Fixed points, periodic points and chaotic dynamics for continuous maps with applications to population dynamics1 Introduction; 2 Notation; 3 Search of fixed points for maps expansive along one direction; 4 The planar case; 4.1 Stretching along the paths and variants; 4.2 The Crossing Lemma; 5 The N-dimensional setting: Intersection Lemma; 5.1 Zero-sets of maps depending on parameters; 5.2 Stretching along the paths in the N-dimensional case; 6 Chaotic dynamics for continuous maps; 7 Definitions and main results; 8 Symbolic dynamics; 9 On various notions of chaos; 10 Linked twist maps. 11 Examples from the ODEs12 Predator-prey model; 12.1 The effects of a periodic harvesting; 12.2 Technical details and proofs; Bibliography; Index. This book facilitates research in the general area of population dynamics by presenting some of the recent developments involving theories, methods and application in this important area of research. The underlying common feature of the studies included in the book is that they are related, either directly or indirectly, to the well-known Lotka-Volterra systems which offer a variety of mathematical concepts from both theoretical and application points of view. Print version record. Includes bibliographical references and index. Lotka-Volterra equations. http://id.loc.gov/authorities/subjects/sh2011003271 Population biology Mathematical models. Biologie des populations Modèles mathématiques. NATURE Ecology. bisacsh NATURE Ecosystems & Habitats Wilderness. bisacsh SCIENCE Environmental Science. bisacsh SCIENCE Life Sciences Ecology. bisacsh Lotka-Volterra equations fast Population biology Mathematical models fast Kolmogorovsche Differentialgleichungen gnd http://d-nb.info/gnd/4164698-8 Volterra-Gleichungen gnd http://d-nb.info/gnd/4137459-9 Populationsdynamik gnd http://d-nb.info/gnd/4046803-3 Lotka-Volterra System. Population Dynamics. Lisena, Benedetta. Pireddu, Marina. Zanolin, Fabio. Ahmad, Shair. http://id.loc.gov/authorities/names/n80048820 Stamova, Ivanka. http://id.loc.gov/authorities/names/no2010079775 has work: Lotka-Volterra and Related Systems (Text) https://id.oclc.org/worldcat/entity/E39PCGqRBXMx97jjKYGvxxgrmd https://id.oclc.org/worldcat/ontology/hasWork Print version: Hou, Zhanyuan. Lotka-Volterra and Related Systems : Recent Developments in Population Dynamics. Berlin : De Gruyter, ©2013 9783110269512 De Gruyter series in mathematics and life sciences. http://id.loc.gov/authorities/names/n2013182704 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=604282 Volltext |
| spellingShingle | Hou, Zhanyuan Lotka-Volterra and Related Systems : Recent Developments in Population Dynamics. De Gruyter series in mathematics and life sciences. Preface; Permanence, global attraction and stability; 1 Introduction; 2 Existence of a compact uniform attractor; 3 Proof of Theorems 2.1, 2.2 and 2.3; 4 Partial permanence and permanence; 5 Necessary conditions for permanence of Lotka-Volterra systems; 6 Sufficient condition for permanence of Lotka-Volterra systems; 7 Further notes; 8 Global attraction and stability of Lotka-Volterra systems; 9 Global stability by Lyapunov functions; 10 Global stability by split Lyapunov functions; 10.1 Checking the conditions (10.2) and (10.8); 10.2 Examples. 11 Global stability of competitive Lotka-Volterra systems12 Global attraction of competitive Lotka-Volterra systems; 13 Some notes; Bibliography; Competitive Lotka-Volterra systems with periodic coefficients; 1 Introduction; 2 The autonomous model. The logistic equation; 3 Two species periodic models; 4 Competitive exclusion; 5 One species extinction in three-dimensional models; 6 The impulsive logistic equation; 7 Two species systems with impulsive effects. A look at the N-dimensional case; 8 The influence of impulsive perturbations on extinction in three-species models; Bibliography. Fixed points, periodic points and chaotic dynamics for continuous maps with applications to population dynamics1 Introduction; 2 Notation; 3 Search of fixed points for maps expansive along one direction; 4 The planar case; 4.1 Stretching along the paths and variants; 4.2 The Crossing Lemma; 5 The N-dimensional setting: Intersection Lemma; 5.1 Zero-sets of maps depending on parameters; 5.2 Stretching along the paths in the N-dimensional case; 6 Chaotic dynamics for continuous maps; 7 Definitions and main results; 8 Symbolic dynamics; 9 On various notions of chaos; 10 Linked twist maps. 11 Examples from the ODEs12 Predator-prey model; 12.1 The effects of a periodic harvesting; 12.2 Technical details and proofs; Bibliography; Index. Lotka-Volterra equations. http://id.loc.gov/authorities/subjects/sh2011003271 Population biology Mathematical models. Biologie des populations Modèles mathématiques. NATURE Ecology. bisacsh NATURE Ecosystems & Habitats Wilderness. bisacsh SCIENCE Environmental Science. bisacsh SCIENCE Life Sciences Ecology. bisacsh Lotka-Volterra equations fast Population biology Mathematical models fast Kolmogorovsche Differentialgleichungen gnd http://d-nb.info/gnd/4164698-8 Volterra-Gleichungen gnd http://d-nb.info/gnd/4137459-9 Populationsdynamik gnd http://d-nb.info/gnd/4046803-3 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh2011003271 http://d-nb.info/gnd/4164698-8 http://d-nb.info/gnd/4137459-9 http://d-nb.info/gnd/4046803-3 |
| title | Lotka-Volterra and Related Systems : Recent Developments in Population Dynamics. |
| title_auth | Lotka-Volterra and Related Systems : Recent Developments in Population Dynamics. |
| title_exact_search | Lotka-Volterra and Related Systems : Recent Developments in Population Dynamics. |
| title_full | Lotka-Volterra and Related Systems : Recent Developments in Population Dynamics. |
| title_fullStr | Lotka-Volterra and Related Systems : Recent Developments in Population Dynamics. |
| title_full_unstemmed | Lotka-Volterra and Related Systems : Recent Developments in Population Dynamics. |
| title_short | Lotka-Volterra and Related Systems : |
| title_sort | lotka volterra and related systems recent developments in population dynamics |
| title_sub | Recent Developments in Population Dynamics. |
| topic | Lotka-Volterra equations. http://id.loc.gov/authorities/subjects/sh2011003271 Population biology Mathematical models. Biologie des populations Modèles mathématiques. NATURE Ecology. bisacsh NATURE Ecosystems & Habitats Wilderness. bisacsh SCIENCE Environmental Science. bisacsh SCIENCE Life Sciences Ecology. bisacsh Lotka-Volterra equations fast Population biology Mathematical models fast Kolmogorovsche Differentialgleichungen gnd http://d-nb.info/gnd/4164698-8 Volterra-Gleichungen gnd http://d-nb.info/gnd/4137459-9 Populationsdynamik gnd http://d-nb.info/gnd/4046803-3 |
| topic_facet | Lotka-Volterra equations. Population biology Mathematical models. Biologie des populations Modèles mathématiques. NATURE Ecology. NATURE Ecosystems & Habitats Wilderness. SCIENCE Environmental Science. SCIENCE Life Sciences Ecology. Lotka-Volterra equations Population biology Mathematical models Kolmogorovsche Differentialgleichungen Volterra-Gleichungen Populationsdynamik |
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