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The major study by Bordo and Helbing (2003) analyses the business cycle in Western economies 1881-2001. They examine four distinct periods in economic history, and conclude that there is a secular trend towards greater synchronisation for…
A framework for the mathematical modeling of evolution in group structured populations is introduced. The population is divided into a fixed large number of groups of fixed size. From generation to generation, new groups are formed that…
The Verhulst model is probably the best known macroscopic rate equation in population ecology. It depends on two parameters, the intrinsic growth rate and the carrying capacity. These parameters can be estimated for different populations…
We study a minimalist kinetic model for economies. A system of agents with local trading rules display emergent demand behaviour. We examine the resulting wealth distribution to look for non-thermal behaviour. We compare and contrast this…
The hypothetical global delivery schedule of Santa Claus must follow strict rolling night-time windows that vary with the Earth's rotation and obey an energy budget that depends on payload size and cruising speed. To design this schedule,…
Blockchain and general purpose distributed ledgers are foundational technologies which bring significant innovation in the infrastructures and other underpinnings of our socio-economic systems. These P2P technologies are able to securely…
The temporal rich club (TRC) phenomenon is widespread in real systems, forming a tight and continuous collection of the prominent nodes that control the system. However, there is still a lack of sufficient understanding of the mechanisms of…
Since the 1940's there has been an interest in the question why social networks often give rise to two antagonistic factions. Recently a dynamical model of how and why such a balance might occur was developed. This note provides an…
Major revolts have recently erupted in parts of the Middle East with substantial international repercussions. Predicting, coping with and winning those revolts have become a grave problem for many regimes and for world powers. We propose a…
We discuss relaxation and aging processes in the one- and two-dimensional $ABC$ models. In these driven diffusive systems of three particle types, biased exchanges in one direction yield a coarsening process characterized in the long time…
The adaptation of biological species to their environment depends on their traits. When various biological processes occur (survival, reproduction, migration, etc.), the trait distribution may change with respect to time and space. In the…
We apply the formalism of the continuous time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time…
We model the dynamics of the cryptocurrency (CC) asset class via a stochastic volatility with correlated jumps (SVCJ) model with rolling-window parameter estimates. By analyzing the time-series of parameters, stylized patterns are…
Structured populations are ubiquitous across the biological sciences. Mathematical models of these populations allow us to understand how individual physiological traits drive the overall dynamics in aggregate. For example, linear age- or…
The aim of this work is to establish the personal income distribution from the elementary constituents of a free market; products of a representative good and agents forming the economic network. The economy is treated as a self-organized…
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…
In large asexual populations, multiple beneficial mutations arise in the population, compete, interfere with each other, and accumulate on the same genome, before any of them fix. The resulting dynamics, although studied by many authors, is…
We introduce a minimal Agent Based Model for financial markets to understand the nature and Self-Organization of the Stylized Facts. The model is minimal in the sense that we try to identify the essential ingredients to reproduce the main…
Simple agent based exchange models are a commonplace in the study of wealth distribution of artificial societies. Generally, each agent is characterized by its wealth and by a risk-aversion factor, and random exchanges between agents allow…
The aim of our study is to describe the dynamics of ant battles, with reference to laboratory experiments, by means of a chemical stochastic model. We focus on ants behavior as an interesting topic in order to predict the ecological…