Related papers: Exactly solvable models through the generalized em…
We consider general models of coupled reaction-diffusion systems for interacting variants of the same species. When the total population becomes large with intensive competition, we prove that the frequencies (i.e. proportions) of the…
Phylogenetic varieties related to equivariant substitution models have been studied largely in the last years. One of the main objectives has been finding a set of generators of the ideal of these varieties, but this has not yet been…
A new strongly correlated electron model is presented. This is formed by two types of sites: one where double occupancy is forbidden, as in the t-J model, and the other where double occupancy is allowed but vacancy is not allowed, as an…
A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be…
Multispecies ecosystems modelled by generalized Lotka-Volterra equations exhibit stationary population abundances, where large number of species often coexist. Understanding the precise conditions under which this is at all feasible and…
Diffusion mediated reaction models are particularly ubiquitous in the description of physical, chemical or biological processes. The random walk schema is a useful tool for formulating these models. Recently, evanescent random walk models…
The one-dimensional coagulation-diffusion process describes the strongly fluctuating dynamics of particles, freely hopping between the nearest-neighbour sites of a chain such that one of them disappears with probability 1 if two particles…
We study a model of a multi-species ecosystem described by Lotka-Volterra-like equations. Interactions among species form a network whose evolution is determined by the dynamics of the model. Numerical simulations show power-law…
Neutral models for the dynamics of a system of competing species are used, nowadays, to describe a wide variety of empirical communities. These models are used in many situations, ranging from population genetics and ecological biodiversity…
An exact formula for the distribution of lifetimes in coherent-noise models and related models is derived. For certain stress distributions, this formula can be analytically evaluated and yields simple closed expressions. For those types of…
Presented here is the explicit solution to the continuous time approximation of the Albert-Barab\'asi scale-free network model at any time t. The solution is found by recursively solving the differential equations via integrating factors,…
It is well known that rather general mutation-recombination models can be solved algorithmically (though not in closed form) by means of Haldane linearization. The price to be paid is that one has to work with a multiple tensor product of…
The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of…
Models relating to the Species-Area curve are usually defined at the species level, and concerned only with ecological timescales. We examine an individual-based model of co-evolution on a spatial lattice based on the Tangled Nature model,…
In this paper, we present a study on how to develop an efficient multiscale simulation strategy for the dynamics of chemically active systems on low-dimensional supports. Such reactions are encountered in a wide variety of situations,…
We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. The purpose of this article is twofold: first, it aims at a…
The convergence to equilibrium of mass action reaction-diffusion systems arising from networks of chemical reactions is studied. The considered reaction networks are assumed to satisfy the detailed balance condition and have no boundary…
It is possible to solve the Einstein constraint equations as an evolutionary rather than an elliptic system. Here we consider the Gauss constraint in electrodynamics as a toy model for thist. We use a combination of the evolutionary method…
Understanding the behaviors of ecological systems is challenging given their multi-faceted complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random interactions have been investigated by the dynamical…
We introduce a new methodology to design uniformly accurate methods for oscillatory evolution equations. The targeted models are envisaged in a wide spectrum of regimes, from non-stiff to highly-oscillatory. Thanks to an averaging…