| Description |
1 online resource (244 pages). |
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text file |
| Series |
De Gruyter Series in Mathematics and Life Sciences
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De Gruyter series in mathematics and life sciences.
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| 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. |
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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. |
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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. |
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11 Examples from the ODEs12 Predator-prey model; 12.1 The effects of a periodic harvesting; 12.2 Technical details and proofs; Bibliography; Index. |
| Summary |
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. |
| Bibliography |
Includes bibliographical references and index. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Lotka-Volterra equations.
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Lotka-Volterra equations. |
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Population biology -- Mathematical models.
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Population biology -- Mathematical models. |
| Genre/Form |
Electronic books.
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Electronic books.
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| Added Author |
Lisena, Benedetta.
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Pireddu, Marina.
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Zanolin, Fabio.
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Ahmad, Shair.
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Stamova, Ivanka.
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| Other Form: |
Print version: Hou, Zhanyuan. Lotka-Volterra and Related Systems : Recent Developments in Population Dynamics. Berlin : De Gruyter, ©2013 9783110269512 |
| ISBN |
9783110269840 (electronic book) |
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3110269848 (electronic book) |
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9783110269512 (alkaline paper) |
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