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In this article, we study the dynamics of marking in football matches. To do this, we surveyed and analyzed 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 characterized a scaling law for the average shape of the fluctuations, unveiling the emergence of complexity in the system. Moreover, we proposed 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.

In this work we study the effect of a traffic light system on the flow of a single lane road by proposing a traffic model based on a cellular automaton that also includes behavioral considerations. We focus on the macroscopic characterization of the system by studying the changes in vehicle density and the occurrence of jams. In this context we observe and characterize a phase transition between the free flow and jammed states. This transition is induced by the instabilities originated by the vehicles stopping at the traffic lights. Moreover, we analyze the effect of these instabilities on the critical density of vehicles at which the transition occurs as a function of two parameters: (i) the in-flow of cars, (ii) the drivers' behavior. For the latter we observe that the traffic light perturbations feedback on the drivers behavior can lead the system to different scenarios, which are also analyzed.

Inspired by real scenarios in Northern Patagonia, we analyze a mathematical model of a simple trophic web with two herbivores and one predator. The studied situations represent a common practice in the steppes of Argentine Patagonia, where livestock are raised in a semi-wild state, either on the open range or enclosed, coexisting with competitors and predators. In the present work, the competing herbivores represent sheep and guanacos, while the predator is associated with the puma. The proposed model combines the concepts of metapopulations and patches dynamics, and includes an explicit hierarchical competition between species, which affects their prospect to colonize an empty patch when having to compete with other species. We perform numerical simulations of spatially extended metapopulations assemblages of the system, which allow us to incorporate the effects of habitat heterogeneity and destruction. The numerical results are compared with those obtained from mean field calculations. We find that the model provides a good theoretical framework in several situations, including the control of the wild populations that the ranchers exert to different extent. Furthermore, the present formulation incorporates new terms in previously analyzed models, that help to reveal the important effects due to the heterogeneous nature of the system.

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.

In the last years the Prisoner Dilemma (PD) has become a paradigm for the study of the emergence of cooperation in spatially structured populations. Such 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 test the dependence of the success of cooperation with the clustering coefficient of the network, for several different families of networks. We have found that this dependence is far from trivial. Additionally, for both stochastic and deterministic dynamics we have also found 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).

Recent studies have established an apparent relationship between the repertoire of signals used for communication and neocortex size of different species of primates and the topology of the social network formed by the interactions between individuals. Inspired by these results, we have developed a model that qualitatively reproduces these observations. The model presents the social organization as a self organized processes where the size of the repertoire in one case and of the neocortex in another play a highly relevant role.

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 to explain 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 barycenter of the respective countries.

Inspired by Axelrod's model of culture dissemination, we introduce and analyze a model for a population of coupled oscillators where different levels of synchronization can be assimilated to different degrees of cultural organization. The state of each oscillator is represented by a set of phases, and the interaction --which occurs between homologous phases-- is weighted by a decreasing function of the distance between individual states. Both ordered arrays and random networks are considered. We find that the transition between synchronization and incoherent behaviour is mediated by a clustering regime with rich organizational structure, where some of the phases of a given oscillator can be synchronized to a certain cluster, while its other phases are synchronized to different clusters., Comment: 6 pages, 5 figures

We study the dynamics of the transmission of the hanta virus infection among mouse populations, taking into account, simultaneously, seasonal variations of the environment and interactions within two classes in the mouse population: adults and subadults. The interactions considered are not symmetric between the two age-organized classes and are responsible for driving the younger members away from home ranges. We consider the case of a bounded habitat affected by seasonal variations., Comment: 6 pages, 7 figures

We investigate possible effects of high order nonlinearities on the shapes of infection refugia of the Hantavirus epidemic. We replace Fisher-like equations that have been recently used to describe Hantavirus spread in mouse populations by generalizations capable of describing Allee effects that are a consequence of the high order nonlinearities. We analyze the equations to calculate steady state solutions. We study the stability of those solutions under physical conditions and compare to the earlier Fisher-like case. We consider spatial modulation of the environment and find that unexpected results appear, including a bifurcation that has not been studied before., Comment: 4 figure

In this work we present an analysis of a spatially non homogeneous ultimatum game. By considering different underlying topologies as substrates on top of which the game takes place we obtain nontrivial behaviors for the evolution of the strategies of the players. We analyze separately the effect of the size of the neighborhood and the spatial structure. Whereas this last effect is the most significant one, we show that even for disordered networks and provided the neighborhood of each site is small, the results can be significantly different from those obtained in the case of fully connected networks., Comment: 6 pages, 5 figures

In this work we present a model for evolving networks, where the driven force is related to the social affinity between individuals in a population. In the model, a set of individuals initially arranged on a regular ordered network and thus linked with their closest neighbors are allowed to rearrange their connections according to a dynamics closely related to that of the stable marriage problem. We show that the behavior of some topological properties of the resulting networks follows a non trivial pattern., Comment: 6 pages, 4 figures included

Different models to study the wealth distribution in an artificial society have considered a transactional dynamics as the driving force. Those models include a risk aversion factor, but also a finite probability of favoring the poorer agent in a transaction. Here we study the case where the partners in the transaction have a previous knowledge of the winning probability and adjust their risk aversion taking this information into consideration. The results indicate that a relatively equalitarian society is obtained when the agents risk in direct proportion to their winning probabilities. However, it is the opposite case that delivers wealth distribution curves and Gini indices closer to empirical data. This indicates that, at least for this very simple model, either agents have no knowledge of their winning probabilities, either they exhibit an ``irrational'' behavior risking more than reasonable., Comment: 7 pages, 8 figures

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., Comment: 8 pages, 9 figures included

We present a model for the description of the evolution of contacts among individuals in a network. At each time step each individual is associated with a domain or neighborhood of fully connected agents.The dynamics of this changing neighborhood will later be translated into a situation where the links between individuals are also dynamic. A characterization in terms of the parameters that govern the evolution of the network and a comparison to previous work on Small World networks is presented as well., Comment: 5 pages, 5 figures

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 spatio-temporal structures emerge, with interesting features which depend on the interplay of separately controllable aspects of the externally imposed environmental changes., Comment: 7 pages, 8 figures, included

Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We first show how stability arguments yield a condition for pattern formation involving the ratio of the pattern wavelength and the effective diffusion length of the individuals. We develop a mode-mode coupling analysis which might be useful in shedding some light on the observed formation of small-amplitude versus large-amplitude patterns., Comment: 4 pages, 2 figures included

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 non-local, 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., Comment: 4 Pages, 6 Figures included

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 the 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., Comment: 5 pages, 3 figs. included

We both show 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 the Chlorite-Tetrathionate reaction, where autocatalytic species 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 behavior. The latter model provides quantitative agreement with the experiments., Comment: 19 pages + 9 figures

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 of noise tuning., Comment: 4 pages, 3 figures