Complexity emerges in measures of the marking dynamics in football games.

In this article, we study the dynamics of marking in football matches. To do this, we survey and analyze a database containing the trajectories of players from both teams on the field of play during three professional games. We describe the dynamics through the construction of temporal bipartite networks of proximity. Based on the introduced concept of proximity, the nodes are the players, and the links are defined between opponents that are close enough to each other at a given moment. By studying the evolution of the heterogeneity parameter of the networks during the game, we characterize a scaling law for the average shape of the fluctuations, unveiling the emergence of complexity in the system. Moreover, we propose a simple model to simulate the players' motion in the field from where we obtained the evolution of a synthetic proximity network. We show that the model captures with a remarkable agreement the complexity of the empirical case, hence it proves to be helpful to elucidate the underlying mechanisms responsible for the observed phenomena.

Game theory in models of pedestrian room evacuation.

We analyze the pedestrian evacuation of a rectangular room with a single door considering a lattice gas scheme with the addition of behavioral aspects of the pedestrians. The movement of the individuals is based on random and rational choices and is affected by conflicts between two or more agents that want to advance to the same position. Such conflicts are solved according to certain rules closely related to the concept of strategies in game theory, cooperation and defection. We consider game rules analogous to those from the Prisoner's Dilemma and Stag Hunt games, with payoffs associated to the probabilities of the individuals to advance to the selected site. We find that, even when defecting is the rational choice for any agent, under certain conditions, cooperators can take advantage from mutual cooperation and leave the room more rapidly than defectors.

Relationship between clustering coefficient and the success of cooperation in networks.

In recent years the prisoner's dilemma has become a paradigm for the study of the emergence of cooperation in spatially structured populations. Such a structure is usually assumed to be given by a graph. In general, the success of cooperative strategies is associated with the possibility of forming globular clusters, which in turn depends on a feature of the network that is measured by its clustering coefficient. In this work we study the dependence of the success of cooperation on this coefficient for regular networks. Additionally, for both stochastic and deterministic dynamics we show that there is a strong dependence on the initial composition of the population. This hints at the existence of several different mechanisms that could promote or hinder cluster expansion. We have studied in detail some of these mechanisms by concentrating on completely ordered networks (large clustering coefficient) or completely random networks (vanishing clustering coefficient).

A model for the emergence of geopolitical division.

In this work, we present a model based on a competitive dynamics that intends to imitate the processes leading to some characteristics of the geopolitical division. The model departs from very simple principles of geopolitical theory and geometrical considerations, but succeeds in explaining the general features related to the actual process. At the same time, we will propose an evolutionary explanation to the fact that most capitals (in Eurasia) are located far from the borders or coasts and, in many cases, close to the barycentre of the respective countries.

Theory of possible effects of the Allee phenomenon on the population of an epidemic reservoir.

We investigate possible effects of high-order nonlinearities on the shapes of infection refugia of the reservoir of an infectious disease. We replace Fisher-type equations that have been recently used to describe, among others, the Hantavirus spread in mouse populations by generalizations capable of describing Allee effects that are a consequence of the high-order nonlinearities. After analyzing the equations to calculate steady-state solutions, we study the stability of those solutions and compare to the earlier Fisher-type case. Finally, we consider the spatial modulation of the environment and find that unexpected results appear, including a bifurcation that has not been studied before.

Cultural propagation on social networks.

In this work we present a model for the propagation of culture on networks of different topology and by considering different underlying dynamics. We extend a previous model proposed by Axelrod by letting a majority govern the dynamics of changes. This in turn allows us to define a Lyapunov functional for the system.

Periodically varying externally imposed environmental effects on population dynamics.

Effects of externally imposed periodic changes in the environment on population dynamics are studied with the help of a simple model. The environmental changes are represented by the temporal and spatial dependence of the competition terms in a standard equation of evolution. Possible applications of the analysis are on the one hand to bacteria in Petri dishes and on the other to rodents in the context of the spread of the Hantavirus epidemic. The analysis shows that spatiotemporal structures emerge, with interesting features which depend on the interplay of separately controllable aspects of the externally imposed environmental changes.

Nonlocal interaction effects on pattern formation in population dynamics.

We consider a model for population dynamics such as for the evolution of bacterial colonies which is of the Fisher type but where the competitive interaction among individuals is nonlocal, and show that spatial structures with interesting features emerge. These features depend on the nature of the competitive interaction as well as on its range, specifically on the presence or absence of tails in, and the central curvature of, the influence function of the interaction.

Applicability of the Fisher equation to bacterial population dynamics.

The applicability of the Fisher equation, which combines diffusion with logistic nonlinearity, to population dynamics of bacterial colonies is studied with the help of explicit analytic solutions for the spatial distribution of a stationary bacterial population under a static mask. The mask protects bacteria from ultraviolet light. The solution, which is in terms of Jacobian elliptic functions, is used to provide a practical prescription to extract Fisher equation parameters from observations and to decide on the validity of the Fisher equation.

Dynamical effects induced by long range activation in a nonequilibrium reaction-diffusion system.

We show both experimentally and numerically that the time scales separation introduced by long range activation can induce oscillations and excitability in nonequilibrium reaction-diffusion systems that would otherwise only exhibit bistability. Namely, we show that in the chlorite-tetrathionate reaction, where the autocatalytic species H+ diffuses faster than the substrates, the spatial bistability domain in the nonequilibrium phase diagram is extended with oscillatory and excitability domains. A simple model and a more realistic model qualitatively account for the observed dynamical behavior. The latter model provides quantitative agreement with the experiments.

Experimental evidence of stochastic resonance without tuning due to non-Gaussian noises.

In order to test theoretical predictions, we have studied the phenomenon of stochastic resonance in an electronic experimental system driven by white non-Gaussian noise. In agreement with the theoretical predictions our main findings are an enhancement of the sensibility of the system together with a remarkable widening of the response (robustness). This implies that even a single resonant unit can reach a marked reduction in the need for noise tuning.

Spatial bistability and waves in a reaction with acid autocatalysis.

The phenomenon of spatial bistability has recently been proposed for a comprehensive understanding of a number of chemical patterns observed in open spatial reactors consisting of thin films of gel diffusively fed from one side. We study experimentally and numerically this phenomenon in the tetrathionate-chlorite reaction characterized by an acid superautocatalysis. We focus on the similarities and differences with previous studies on the chlorine dioxide-iodide reaction. In addition, we show that this reaction, which is only bistable in a continuous stirred tank reactor, can exhibit oscillatory and traveling waves when diffusion comes into play. Our computations suggest that the nonstationary behaviour originates from differential diffusive transport.

An exact analytical solution of a three-component model for competitive coexistence.

A three-component competition system is modeled as a reaction-diffusion process. An exact analytical solution has been found that indicates that in certain situations the classical results on extinction and coexistence of Lotka-Volterra-type equations are no longer valid. Cases with one or both predators diffuse are analyzed, and the stability question is discussed.