Minimal mechanisms for vegetation patterns in semiarid regions

The minimal ecological requirements for formation of regular vegetation patterns in semiarid systems have been recently questioned. Against the general belief that a combination of facilitative and competitive interactions is necessary, recent theoretical studies suggest that, under broad conditions, nonlocal competition among plants alone may induce patterns. In this paper, we review results along this line, presenting a series of models that yield spatial patterns when finite-range competition is the only driving force. A preliminary derivation of this type of model from a more detailed one that considers water-biomass dynamics is also presented. Keywords: Vegetation patterns, nonlocal interactionsComment: 8 pages, 4 figure

Numerical Study of a Lyapunov Functional for the Complex Ginzburg-Landau Equation

We numerically study in the one-dimensional case the validity of the functional calculated by Graham and coworkers as a Lyapunov potential for the Complex Ginzburg-Landau equation. In non-chaotic regions of parameter space the functional decreases monotonically in time towards the plane wave attractors, as expected for a Lyapunov functional, provided that no phase singularities are encountered. In the phase turbulence region the potential relaxes towards a value characteristic of the phase turbulent attractor, and the dynamics there approximately preserves a constant value. There are however very small but systematic deviations from the theoretical predictions, that increase when going deeper in the phase turbulence region. In more disordered chaotic regimes characterized by the presence of phase singularities the functional is ill-defined and then not a correct Lyapunov potential.Comment: 20 pages,LaTeX, Postcript version with figures included available at http://formentor.uib.es/~montagne/textos/nep

Preface "Nonlinear processes in oceanic and atmospheric flows"

Nonlinear phenomena are essential ingredients in many oceanic and atmospheric processes, and successful understanding of them benefits from multidisciplinary collaboration between oceanographers, meteorologists, physicists and mathematicians. The present Special Issue on ``Nonlinear Processes in Oceanic and Atmospheric Flows'' contains selected contributions from attendants to the workshop which, in the above spirit, was held in Castro Urdiales, Spain, in July 2008. Here we summarize the Special Issue contributions, which include papers on the characterization of ocean transport in the Lagrangian and in the Eulerian frameworks, generation and variability of jets and waves, interactions of fluid flow with plankton dynamics or heavy drops, scaling in meteorological fields, and statistical properties of El Ni\~no Southern Oscillation.Comment: This is the introductory article to a Special Issue on "Nonlinear Processes in Oceanic and Atmospheric Flows'', published in the journal Nonlinear Processes in Geophysics, where the different contributions are summarized. The Special Issue itself is freely available from http://www.nonlin-processes-geophys.net/special_issue103.htm

Biological activity in the wake of an island close to a coastal upwelling

Hydrodynamic forcing plays an important role in shaping the dynamics of marine organisms, in particular of plankton. In this work we study the planktonic biological activity in the wake of an island which is close to an upwelling region. Our research is based on numerical analysis of a kinematic flow mimicking the hydrodynamics in the wake, coupled to a three-component plankton model. Depending on model parameters different phenomena are described: a) The lack of transport of nutrients and plankton across the wake, so that the influence of upwelling on primary production on the other side of the wake is blocked. b) For sufficiently high vorticity, the role of the wake in facilitating this transport and leading to an enhancement of primary production. Finally c) we show that under certain conditions the interplay between wake structures and biological growth leads to plankton blooms inside mesoscale hydrodynamic vortices that act as incubators of primary production.Comment: 42 pages, 9 figure

Plankton blooms in vortices: The role of biological and hydrodynamic time scales

We study the interplay of hydrodynamic mesoscale structures and the growth of plankton in the wake of an island, and its interaction with a coastal upwelling. Our focus is on a mechanism for the emergence of localized plankton blooms in vortices. Using a coupled system of a kinematic flow mimicking the mesoscale structures behind the island and a simple three component model for the marine ecosystem, we show that the long residence times of nutrients and plankton in the vicinity of the island and the confinement of plankton within vortices are key factors for the appearance of localized plankton bloomsComment: 29 pages, 9 figure

Wave-unlocking transition in resonantly coupled complex Ginzburg-Landau equations

We study the effect of spatial frequency-forcing on standing-wave solutions of coupled complex Ginzburg-Landau equations. The model considered describes several situations of nonlinear counterpropagating waves and also of the dynamics of polarized light waves. We show that forcing introduces spatial modulations on standing waves which remain frequency locked with a forcing-independent frequency. For forcing above a threshold the modulated standing waves unlock, bifurcating into a temporally periodic state. Below the threshold the system presents a kind of excitability.Comment: 4 pages, including 4 postscript figures. To appear in Physical Review Letters (1996). This paper and related material can be found at http://formentor.uib.es/Nonlinear