Related papers: Diffusion-driven demographics -- Turing model as a…

Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…

We present a stochastic two-population model that describes the migration and growth of semi-sedentary foragers and sedentary farmers along a river valley during the Neolithic transition. The main idea of this paper is that random migration…

Human settlements on Earth are scattered in a multitude of shapes, sizes and spatial arrangements. These patterns are often not random but a result of complex geographical, cultural, economic and historical processes that have profound…

The most profound change in the relationship between humans and their environment was the introduction of agriculture and pastoralism. [....] For an understanding of the expansion process, it appears appropriate to apply a diffusive model.…

Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…

As proposed by Alan Turing in 1952 as a ubiquitous mechanism for nonequilibrium pattern formation, diffusional effects may destabilize uniform distributions of reacting chemical species and lead to both spatially and temporally…

In the present article, we investigate the effects of dormancy on an abstract population genetic level. We first provide a short review of seed bank models in population genetics, and the role of dormancy for the interplay of evolutionary…

Turing instabilities for a two species reaction-diffusion systems is studied under anisotropic diffusion. More specifically, the diffusion constants which characterize the ability of the species to relocate in space are direction sensitive.…

The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…

This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the spatial epidemic model by Turing mechanisms. In particular, we present theoretical analysis to results of the numerical…

Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction--diffusion theory, which connects cellular signalling and transport…

Models of ordering dynamics allow to understand natural systems in which an initially disordered population homogenizes some traits via local interactions. The simplest of these models, with wide applications ranging from evolutionary to…

Urban displacement - when a household is forced to relocate due to conditions affecting its home or surroundings - often results from rising housing costs, particularly in wealthy, prosperous cities. However, its dynamics are complex and…

Land use expansion is linked to major sustainability concerns including climate change, food security and biodiversity loss. This expansion is largely concentrated in so-called frontiers, defined here as places experiencing marked…

We study how changes in population size and fluctuating environmental conditions influence the establishment of seed banks in plants. Our model is a modification of the Wright-Fisher model with seed bank, introduced by Kaj, Krone and…

Self-organization, the ability of a system of microscopically interacting entities to shape macroscopically ordered structures, is ubiquitous in Nature. Spatio-temporal patterns are abundantly observed in a large plethora of applications,…

Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…

This study investigates the complex dynamic interactions between two typed populations coexisting within a shared space. We propose both theoretical and numerical study to analyze scenarios where one population (population $1$) must…

In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…

We present a general, physically motivated non-linear and non-local advection equation in which the diffusion of interacting random walkers competes with a local drift arising from a kind of peer pressure. We show, using a mapping to an…