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We introduce a simple model of population dynamics which considers reproducing individuals or particles with birth and death rates depending on the number of other individuals in their neighborhood. The model shows an inhomogeneous quasistationary pattern with many different clusters of particles arranged periodically in space. We derive the equation for(More)
A central model in theoretical ecology considers the competition of a range of species for a broad spectrum of resources. Recent studies have shown that essentially two different outcomes are possible. Either the species surviving competition are more or less uniformly distributed over the resource spectrum, or their distribution is 'lumped' (or 'clumped'),(More)
We present properties of Lotka-Volterra equations describing ecological competition among a large number of interacting species. First we extend previous stability conditions to the case of a non-homogeneous niche space, i.e. that of a carrying capacity depending on the species trait. Second, we discuss mechanisms leading to species clustering and obtain an(More)
We show that a sonic crystal made of periodic distributions of rigid cylinders in air acts as a new material which allows the construction of refractive acoustic devices for airborne sound. It is demonstrated that, in the long-wave regime, the crystal has low impedance and the sound is transmitted at subsonic velocities. Here, the fabrication and(More)
We study the spatial patterns formed by interacting biological populations or reacting chemicals under the influence of chaotic flows. Multiple species and nonlinear interactions are explicitly considered, as well as cases of smooth and nonsmooth forcing sources. The small-scale structure can be obtained in terms of characteristic Lyapunov exponents of the(More)
Regular vegetation patterns in semiarid ecosystems are believed to arise from the interplay between long-range competition and facilitation processes acting at smaller distances. We show that, under rather general conditions, long-range competition alone may be enough to shape these patterns. To this end we propose a simple, general model for the dynamics(More)
Disorder is an unavoidable ingredient of real systems. Spatial disorder generates Griffiths phases (GPs) which, in analogy to critical points, are characterized by a slow relaxation of the order parameter and divergences of quantities such as the susceptibility. However, these singularities appear in an extended region of the parameter space and not just at(More)
Population dynamics of individuals undergoing birth and death and diffusing by short- or long-range two-dimensional spatial excursions (Gaussian jumps or Lévy flights) is studied. Competitive interactions are considered in a global case, in which birth and death rates are influenced by all individuals in the system, and in a nonlocal but finite-range case(More)
We study the properties of general Lotka-Volterra models with competitive interactions. The intensity of the competition depends on the position of species in an abstract niche space through an interaction kernel. We show analytically and numerically that the properties of these models change dramatically when the Fourier transform of this kernel is not(More)
Meso- and submesoscales (fronts, eddies, filaments) in surface ocean flow have a crucial influence on marine ecosystems. Their dynamics partly control the foraging behavior and the displacement of marine top predators (tuna, birds, turtles, and cetaceans). In this work we focus on the role of submesoscale structures in the Mozambique Channel in the(More)