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We model the dynamics of the Schelling model for agents described simply by a continuously distributed variable - wealth. Agents move to neighborhoods where their wealth is not lesser than that of some proportion of their neighbors, the…
Challenges due to the rapid urbanization of the world -- especially in emerging countries -- range from an increasing dependence on energy, to air pollution, socio-spatial inequalities, environmental and sustainability issues. Modelling the…
To model the dynamics of polymers formed through nucleation, elongated by polymerisation, shortened by depolymerisation and subject to aggregation reactions, we study a nonlinear integro-differential equation. Growth and shrinkage are…
Economies grow by upgrading the type of products they produce and export. The technology, capital, institutions and skills needed to make such new products are more easily adapted from some products than others. We study the network of…
In complex systems, many different parts interact in non-obvious ways. Traditional research focuses on a few or a single aspect of the problem so as to analyze it with the tools available. To get a better insight of phenomena that emerge…
In this paper we introduce kinetic equations for the evolution of the probability distribution of two goods among a huge population of agents. The leading idea is to describe the trading of these goods by means of some fundamental rules in…
We introduce the logistic model of consumption growth, which captures a negative feedback loop preventing an unlimited growth of consumption due to finite biophysical resources of our planet. This simple dynamic model allows for derivation…
The increasing integration of world economies, which organize in complex multilayer networks of interactions, is one of the critical factors for the global propagation of economic crises. We adopt the network science approach to quantify…
This article conducts a literature review on the topic of monetary policy in developing countries and focuses on the effectiveness of monetary policy in promoting economic growth and the relationship between monetary policy and economic…
Consider the problem of a government that wants to reduce the debt-to-GDP (gross domestic product) ratio of a country. The government aims at choosing a debt reduction policy which minimises the total expected cost of having debt, plus the…
The emergence of labor division in multi-agent system is analyzed by the method of statistical physics. Considering a system consists of N homogeneous agents. Their behaviors are determined by the returns from their production. Using the…
Biological entities are inherently dynamic. As such, various ecological disciplines use mathematical models to describe temporal evolution. Typically, growth curves are modelled as sigmoids, with the evolution modelled by ordinary…
This paper is mainly devoted to lay an empirical foundation for further research on complex spatial dynamics of two-population interaction. Based on the US population census data, a rural and urban population interaction model is developed.…
In this paper, we conduct a thorough mathematical analysis of a tumor growth model with treatments. The model is a system describing the evolution of metastatic tumors and the number of cells present in a primary tumor. The former evolution…
Global trade is shaped by a complex mix of factors beyond supply and demand, including tangible variables like transport costs and tariffs, as well as less quantifiable influences such as political and economic relations. Traditionally,…
This paper studies a mathematical model of city formation by migration of firms and workers. The Core-Periphery model in the new economic geography, which considers the single migration of workers driven by real wage inequality among…
Statistical and mathematical modeling are crucial to describe, interpret, compare and predict the behavior of complex biological systems including the organization of hematopoietic stem and progenitor cells in the bone marrow environment.…
In this paper we study some mathematical models describing evolution of population density and spread of epidemics in population systems in which spatial movement of individuals depends only on the departure and arrival locations and does…
We consider extensive data on Spanish international trades and population composition and, through statistical-mechanics and graph-theory driven analysis, we unveil that the social network made of native and foreign-born individuals plays a…
We consider a moving boundary mathematical model of biological invasion. The model describes the spatiotemporal evolution of two adjacent populations: each population undergoes linear diffusion and logistic growth, and the boundary between…