Search results for "Applied Mathematics"
showing 10 items of 4379 documents
An existence and uniqueness principle for a nonlinear version of the Lebowitz-Rubinow model with infinite maximum cycle length
2017
The present article deals with existence and uniqueness results for a nonlinear evolution initial-boundary value problem, which originates in an age-structured cell population model introduced by Lebowitz and Rubinow (1974) describing the growth of a cell population. Cells of this population are distinguished by age a and cycle length l. In our framework, daughter and mother cells are related by a general reproduction rule that covers all known biological ones. In this paper, the cycle length l is allowed to be infinite. This hypothesis introduces some mathematical difficulties. We consider both local and nonlocal boundary conditions.
A two-point boundary value formulation of a mean-field crowd-averse game
2014
Abstract We consider a population of “crowd-averse” dynamic agents controlling their states towards regions of low density. This represents a typical dissensus behavior in opinion dynamics. Assuming a quadratic density distribution, we first introduce a mean-field game formulation of the problem, and then we turn the game into a two-point boundary value problem. Such a result has a value in that it turns a set of coupled partial differential equations into ordinary differential equations.
FAST OSCILLATING MIGRATIONS IN A PREDATOR-PREY MODEL
1996
The aim of this paper is to give a method which permits us to describe how individual properties can emerge at the population level, in population dynamics. We consider interacting populations. In order to take into account the spatial or behavioral heterogeneity, we subdivide each population into subpopulations. A given subpopulation corresponds to those individuals having the same behavior and who are in a homogeneous environment. Furthermore, we assume that the migration process is faster than the growth and interaction processes. Therefore, we must study models with many variables coupled together into large scaled differential systems. Firstly, our method permits us to reduce these co…
On the qualitative analysis of the solutions of a mathematical model of social dynamics
2006
Abstract This work deals with a family of dynamical systems which were introduced in [M.L. Bertotti, M. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Models Methods Appl. Sci. 7 (2004) 1061–1084], modelling the evolution of a population of interacting individuals, distinguished by their social state. The existence of certain uniform distribution equilibria is proved and the asymptotic trend is investigated.
A Side-by-Side Single Sex Age-Structured Human Population Dynamic Model: Exact Solution and Model Validation
2008
A side-by-side single sex age-structured population dynamic model is presented in this paper. The model consists of two coupled von Foerster-McKendrick-type quasi-linear partial differential equations, two initial conditions, and two boundary conditions. The state variables of the model are male and female population densities. The solutions of these partial differential equations provide explicit time and age dependence of the variables. The initial conditions define the male and female population densities at the initial time, while the boundary conditions compute the male and female births at zero-age by using fertility rates. The assumptions of the nontime-dependence of the death and fe…
ON THE EXISTENCE OF LIMIT CYCLES IN OPINION FORMATION PROCESSES UNDER TIME PERIODIC INFLUENCE OF PERSUADERS
2008
This paper concerns a model of opinion formation in a population of interacting individuals under the influence of external leaders or persuaders, which act in a time periodic fashion. The model is formulated within a general framework inspired to a discrete generalized kinetic approach, which has been developed in Ref. 6. It is expressed by a system of non-autonomous nonlinear ordinary differential equations. The dynamics of such a system is investigated and the existence of a globally asymptotically stable periodic solution is analytically proved in three example cases, each one corresponding to a different quantitative choice of the actions of the persuaders. Equivalently, in three part…
Mathematical modelling of social obesity epidemic in the region of Valencia, Spain
2010
In this article, we analyse the incidence of excess weight in 24- to 65-year-old residents in the region of Valencia, Spain, and predict its behaviour in the coming years. In addition, we present some possible strategies to prevent the spread of the obesity epidemic. We use classical logistic regression analysis to find out that a sedentary lifestyle and unhealthy nutritional habits are the most important causes of obesity in the 24- to 65-year-old population in Valencia. We propose a new mathematical model of epidemiological type to predict the incidence of excess weight in this population in the coming years. Based on the mathematical model sensitivity analysis, some possible general stra…
Propedeutics and practice of research in Methodology programs of undergraduate Sociology degrees in Argentina and other Latin American countries
2020
Los programas de materias de Metodología de la Investigación en carreras universitarias de grado en Sociología, principalmente de Argentina (2018), constituyen el objeto de análisis del presente artículo. Partiendo de interrogantes en torno a los modos en que se enseña a investigar, se escogió analizar programas en tanto documentos que cristalizan y brindan indicios de prácticas y discursos formativos. Si bien los programas distan de las prácticas en las aulas, ofrecen información significativa y permiten ampliar la muestra respecto a la observación in situ. Los resultados del relevamiento se organizaron en dos ejes: las variantes en las propuestas de enseñanza y las maneras de entender las…
Asymptotic Hölder regularity for the ellipsoid process
2020
We obtain an asymptotic Hölder estimate for functions satisfying a dynamic programming principle arising from a so-called ellipsoid process. By the ellipsoid process we mean a generalization of the random walk where the next step in the process is taken inside a given space dependent ellipsoid. This stochastic process is related to elliptic equations in non-divergence form with bounded and measurable coefficients, and the regularity estimate is stable as the step size of the process converges to zero. The proof, which requires certain control on the distortion and the measure of the ellipsoids but not continuity assumption, is based on the coupling method.
Convergence of dynamic programming principles for the $p$-Laplacian
2018
We provide a unified strategy to show that solutions of dynamic programming principles associated to the $p$-Laplacian converge to the solution of the corresponding Dirichlet problem. Our approach includes all previously known cases for continuous and discrete dynamic programming principles, provides new results, and gives a convergence proof free of probability arguments.