Contents
1 Introduction 9
1.1 Vegetation patterns . . . . 9
1.2 Fairy circles . . . . 15
1.2.1 Description . . . . 15
1.2.2 Hypotheses of their formation and maintenance . . 17
2 Eects of strong nonlocal coupling in a bistable model 24 2.1 Strong versus weak nonlocal coupling . . . . 26
2.2 A simple bistable model with strong nonlocal coupling . . . 27
2.3 Symmetry breaking instability . . . . 29
2.4 Single fronts . . . . 31
2.5 Fairy circles . . . . 37
2.6 Flat spots . . . . 41 6
2.7 Conditions for the appearance of fairy circles and at spots 45
2.8 Interaction of fairy circles . . . . 46
3 Fairy circles in vegetation models for arid regions 56 3.1 The strong nonlocal logistic-type model . . . . 57
3.2 Fairy circles in the nonlocal logistic-type model . . . . 60
3.3 Analytical description in the nonlocal logistic-type model . 64 3.4 Numerical simulations of fairy circles in the strong nonlocal reaction-diusion type of model . . . . 66
4 Spots in a semiarid region in the highlands 70 4.1 The logistic-type model . . . . 72
4.2 Spatial instability of the homogeneous state . . . . 74
4.3 Measurement of the parameters . . . . 76
4.4 Localized spots of vegetation . . . . 83
5 Spiral vegetation patterns 87 5.1 Field observations . . . . 88
5.2 Mechanism for excitability . . . . 92
5.3 Mathematical model . . . . 93
5.4 Excitability of the system . . . . 95
5.5 Numerical simulations . . . . 98 7
6 Conclusions and discussion 101
Bibliography 104
7 Appendix 123
8
