相关论文: The modified Klein Gordon equation for neolithic p…

The motion of particles, where the particles: electrons, ions in microtubules or migrated peoples can be described as the superposition of diffusion and ordered waves. In this paper it is shown that the master equation for transport…

The causes and implications of the regional variations in the spread of the incipient agriculture in Europe remain poorly understood. We apply population dynamics models to study the dispersal of the Neolithic in Europe from a localized…

We perform the analysis of a hyperbolic model which is the analog of the Fisher-KPP equation. This model accounts for particles that move at maximal speed $\epsilon^{-1}$ ($\epsilon\textgreater{}0$), and proliferate according to a reaction…

We present a mathematical model, based on the compilation and statistical processing of radiocarbon dates, of the transition from the Mesolithic to the Neolithic, from about 7,000 to 4,000 BC in Europe. The arrival of the Neolithic is…

Farming and herding were introduced to Europe from the Near East and Anatolia; there are, however, considerable arguments about the mechanisms of this transition. Were it people who moved and outplaced the indigenous hunter- gatherer groups…

Two alternative ways of description an evolution constrained by mass-shell equation are given by the hyperbolic and the periodic angles. In the both cases the angles are proportional to the mass. The differential operators with respect to…

We consider parameter estimation for the spread of the Neolithic incipient farming across Europe using radiocarbon dates. We model the arrival time of farming at radiocarbon-dated, early Neolithic sites by a numerical solution to an…

This paper concerns periodic solutions for a 1D-model with nonlocal velocity given by the periodic Hilbert transform. There is a rich literature showing that this model presents singular behavior of solutions via numerics and mathematical…

We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype density as a nonlinear flow in mutation space, combining…

In this paper the spatial-temporal dynamics of the members of interacting populations is described by nonlinear partial differential equations. We consider the migration as a diffusion process influenced by the changing values of the birth…

We consider the discrete-time migration-recombination equation, a deterministic, nonlinear dynamical system that describes the evolution of the genetic type distribution of a population evolving under migration and recombination in a law of…

Inspired by the works of Hughes [17, 18], we formalize and prove the well posedness of a hyperbolic--elliptic system whose solutions describe the dynamics of a moving crowd. The resulting model is here shown to be well posed and the time of…

This paper deals with a nonhomogeneous scalar parabolic equation with possibly degenerate diffusion term; the process has only one stationary state. The equation can be interpreted as modeling collective movements (crowd dynamics, for…

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…

In this article, we are interested in a non-monotone system of logistic reaction-diffusion equations. This system of equations models an epidemics where two types of pathogens are competing, and a mutation can change one type into the other…

We consider a minimal go-or-grow model of cell invasion, whereby cells can either proliferate, following logistic growth, or move, via linear diffusion, and phenotypic switching between these two states is density-dependent. Formal analysis…

The Fisher-KPP model, and generalisations thereof, is a simple reaction-diffusion models of biological invasion that assumes individuals in the population undergo linear diffusion with diffusivity $D$, and logistic proliferation with rate…

The influence of migration on the stochastic dynamics of subdivided populations is still an open issue in various evolutionary models. We develop here a self-consistent mean-field-like method in order to determine the effects of migration…

In this paper, we establish a novel approach to proving existence of non-negative weak solutions for degenerate parabolic equations of fourth order, like the Cahn-Hilliard and certain thin film equations. The considered evolution equations…

The long-run convergence of developing economies toward advanced countries exhibits robust empirical regularities, yet the mechanisms underlying technological diffusion remain insufficiently specified in standard growth models. In this…