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