Lotka-Volterra and Related Systems

1 - Preface [Seite 5]
2 - Permanence, global attraction and stability [Seite 9]
2.1 - 1 Introduction [Seite 9]
2.2 - 2 Existence of a compact uniform attractor [Seite 11]
2.3 - 3 Proof of Theorems 2.1, 2.2 and 2.3 [Seite 16]
2.4 - 4 Partial permanence and permanence [Seite 23]
2.5 - 5 Necessary conditions for permanence of Lotka-Volterra systems [Seite 34]
2.6 - 6 Sufficient condition for permanence of Lotka-Volterra systems [Seite 39]
2.7 - 7 Further notes [Seite 47]
2.8 - 8 Global attraction and stability of Lotka-Volterra systems [Seite 47]
2.9 - 9 Global stability by Lyapunov functions [Seite 48]
2.10 - 10 Global stability by split Lyapunov functions [Seite 50]
2.10.1 - 10.1 Checking the conditions (10.2) and (10.8) [Seite 54]
2.10.2 - 10.2 Examples [Seite 55]
2.11 - 11 Global stability of competitive Lotka-Volterra systems [Seite 56]
2.12 - 12 Global attraction of competitive Lotka-Volterra systems [Seite 63]
2.13 - 13 Some notes [Seite 68]
2.14 - Bibliography [Seite 68]
3 - Competitive Lotka-Volterra systems with periodic coefficients [Seite 71]
3.1 - 1 Introduction [Seite 71]
3.2 - 2 The autonomous model. The logistic equation [Seite 72]
3.3 - 3 Two species periodic models [Seite 76]
3.4 - 4 Competitive exclusion [Seite 84]
3.5 - 5 One species extinction in three-dimensional models [Seite 90]
3.6 - 6 The impulsive logistic equation [Seite 99]
3.7 - 7 Two species systems with impulsive effects. A look at the N-dimensional case [Seite 103]
3.8 - 8 The influence of impulsive perturbations on extinction in three-species models [Seite 117]
3.9 - Bibliography [Seite 129]
4 - Fixed points, periodic points and chaotic dynamics for continuous maps with applications to population dynamics [Seite 131]
4.1 - 1 Introduction [Seite 131]
4.2 - 2 Notation [Seite 133]
4.3 - 3 Search of fixed points for maps expansive along one direction [Seite 135]
4.4 - 4 The planar case [Seite 136]
4.4.1 - 4.1 Stretching along the paths and variants [Seite 136]
4.4.2 - 4.2 The Crossing Lemma [Seite 151]
4.5 - 5 The N-dimensional setting: Intersection Lemma [Seite 160]
4.5.1 - 5.1 Zero-sets of maps depending on parameters [Seite 165]
4.5.2 - 5.2 Stretching along the paths in the N-dimensional case [Seite 171]
4.6 - 6 Chaotic dynamics for continuous maps [Seite 176]
4.7 - 7 Definitions and main results [Seite 180]
4.8 - 8 Symbolic dynamics [Seite 189]
4.9 - 9 On various notions of chaos [Seite 198]
4.10 - 10 Linked twist maps [Seite 206]
4.11 - 11 Examples from the ODEs [Seite 214]
4.12 - 12 Predator-prey model [Seite 215]
4.12.1 - 12.1 The effects of a periodic harvesting [Seite 215]
4.12.2 - 12.2 Technical details and proofs [Seite 223]
4.13 - Bibliography [Seite 233]
5 - Index [Seite 243]