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Fifty years ago, Wilson and Cowan developed a mathematical model to describe the activity of neural populations. In this seminal work, they divided the cells in three groups: active, sensitive and refractory, and obtained a dynamical system…
The role of turbulent effects for dynamos in the Sun and stars continues to be debated. Mean-field (MF) theory provides a broadly used framework to connect these effects to fundamental magnetohydrodynamics. While inaccessible…
We present a comprehensive, nonperturbative analytical method to investigate the dynamics of time-dependent oscillating scalar field configurations. The method is applied to oscillons in a double well Klein-Gordon model in two and three…
This paper focuses on the opinion dynamics under the influence of manipulative agents. This type of agents is characterized by the fact that their opinions follow a trajectory that does not respond to the dynamics of the model, although it…
We introduce a model of multi-agent dynamics for self-organised motion; individuals travel at a constant speed while trying to adopt the averaged body attitude of their neighbours. The body attitudes are represented through unitary…
Two complementary mathematical models for attitude formation are considered: Starting from the model of Weidlich and Haag (1983), which assumes indirect interactions that are mediated by a mean field, a new model is proposed, which is…
People organize in groups and contagions spread across them. A simple stochastic process, yet complex to model due to dynamical correlations within and between groups. Moreover, groups can evolve if agents join or leave in response to…
A microscopic model of interacting oscillators, which admits two conserved quantities, volume, and energy, is investigated. We begin with a system driven by a general nonlinear potential under high-temperature regime by taking the inverse…
We introduce and analyse a three-body consensus model (3CM) for non-linear consensus dynamics on hypergraphs. Our model incorporates reinforcing group effects, which can cause shifts in the average state of the system even in if the…
Understanding how sustainable behaviors spread within heterogeneous societies requires the integration of behavioral data, social influence mechanisms, and structured approaches to control. In this paper, we propose a data-driven…
We present a model describing the temporal evolution of opinions due to interactions among a network of individuals. This Accept-Shift-Constrict (ASC) model is formulated in terms of coupled nonlinear differential equations for opinions and…
In order to drive effectively, a driver must be aware of how they can expect other vehicles' behaviour to be affected by their decisions, and also how they are expected to behave by other drivers. One common family of methods for addressing…
In order to investigate collective effects of interactions between pedestrians and attractions, this study extends the social force model. Such interactions lead pedestrians to form stable clusters around attractions, or even to rush into…
We introduce a mathematical model on the dynamics of demand and supply incorporating collectability and saturation factors. Our analysis shows that when the fluctuation of the determinants of demand and supply is strong enough, there is…
We study binary opinion formation in a large population where individuals are influenced by the opinions of other individuals. The population is characterised by the existence of (i) communities where individuals share some similar…
In this paper, we study collective interaction dynamics emerging in the game of football-soccer. To do so, we surveyed a database containing body-sensors traces measured during three professional football matches, where we observed…
We investigate the detailed dynamics of a truncated $\alpha\omega$ dynamo model with a dynamic $\alpha$ effect. We find the presence of multiple attractors, including two chaotic attractors with a fractal basin boundary which merge to form…
The dynamics of a bouncing ball model under the influence of dissipation is investigated by using a two dimensional nonlinear mapping. When high dissipation is considered, the dynamics evolves to different attractors. The evolution of the…
We study the Markovian process of a multi-mode open system connecting with a non-equilibrium environment, which consists of several heat baths with different temperatures. As an illustration, we study the steady state of three linearly…
Antagonistic crowd behaviors are often observed in cases of serious conflict. Antagonistic emotions, which is the typical psychological state of agents in different roles (i.e. cops, activists, and civilians) in crowd violent scenes, and…