Examinando por Autor "Khalil, Nagi"

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Approach to consensus in models of continuous-opinion dynamics: A study inspired by the physics of granular gases
(Elsevier, 2021) Khalil, Nagi
A model for continuous-opinion dynamics is proposed and studied by taking advantage of its similarities with a mono-dimensional granular gas. Agents interact as in the Deffuant model, with a parameter controlling the persuasibility of the individuals. The interaction coincides with the collision rule of two grains moving on a line, provided opinions and velocities are identified, with being the so-called coefficient of normal restitution. Starting from the master equation of the probability density of all opinions, general conditions are given for the system to reach consensus. The case when the interaction frequency is proportional to the -power of the relative opinions is studied in more detail. It is shown that the mean-field approximation to the master equation leads to the Boltzmann kinetic equation for the opinion distribution. In this case, the system always approaches consensus, which can be seen as the approach to zero of the opinion temperature, a measure of the width of the opinion distribution. Moreover, the long-time behaviour of the system is characterized by a scaling solution to the Boltzmann equation in which all time dependence occurs through the temperature. The case is related to the Deffuant model and is analytically soluble. The scaling distribution is unimodal and independent of . For the distribution of opinions is unimodal below a critical value of , being multimodal with two maxima above it. This means that agents may approach consensus while being polarized. Near the critical points and for , the distribution of opinions is well approximated by the sum of two Gaussian distributions. Monte Carlo simulations are in agreement with the theoretical results.
Cooperation transitions in social games induced by aspiration-driven players
(2024-02-12) Aguilar-Janita, Miguel; Khalil, Nagi; Leyva, Inmaculada; Sendiña-Nadal, Irene
Cooperation and defection are social traits whose evolutionary origin is still unresolved. Recent behavioral experiments with humans suggested that strategy changes are driven mainly by the individuals' expectations and not by imitation. This work theoretically analyzes and numerically explores an aspiration-driven strategy updating in a well-mixed population playing games. The payoffs of the game matrix and the aspiration are condensed into just two parameters that allow a comprehensive description of the dynamics. We find continuous and abrupt transitions in the cooperation density with excellent agreement between theory and the Gillespie simulations. Under strong selection, the system can display several levels of steady cooperation or get trapped into absorbing states. These states are still relevant for experiments even when irrational choices are made due to their prolonged relaxation times. Finally, we show that for the particular case of the prisoner dilemma, where defection is the dominant strategy under imitation mechanisms, the self-evaluation update instead favors cooperation nonlinearly with the level of aspiration. Thus, our work provides insights into the distinct role between imitation and self-evaluation with no learning dynamics.
Deterministic and stochastic cooperation transitions in evolutionary games on networks
(2022) Khalil, Nagi; Leyva, Inmaculada; Almendral, Juan Antonio; Sendiña-Nadal, Irene
The environment has a strong influence on a population's evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continuous change in nature. To model an ever-changing environment, we develop a framework of evolutionary dynamics with stochastic game transitions, where individuals' behaviors together with the games they play in one time step decide the games to be played next time step. Within this framework, we study the evolution of cooperation in structured populations and find a simple rule: natural selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, $b$, to the corresponding cost, $c$, exceeds $k-k'$, which means $b/c>k-k'$, where $k$ is the average number of neighbors and $k'$ captures the effects from game transitions. We show that even if each individual game opposes cooperation, allowing for a transition between them can result in a favorable outcome for cooperation. Even small variations in different games being played can promote cooperation markedly. Our work suggests that interdependence between the environment and the individuals' behaviors may explain the large-scale cooperation in realistic systems even when cooperation is expensive relative to its benefit.
Fluctuations, correlations, and Casimir-like forces in the homogeneous cooling state of a granular gas
(AIP, 2024-01-22) Jiménez Oliva, Jesús David; Rodriguez-Lopez, Pablo; Khalil, Nagi
The fluctuating hydrodynamics by Brey et. al. is analytically solved to get the long-time limit of the fluctuations of the number density, velocity field, and energy density around the homogeneous cooling state of a granular gas, under physical conditions where it keeps stable. Explicit expressions are given for the non-white contributions in the elastic limit. For small dissipation, the latter is shown to be much smaller than the inelastic contributions, in general. The fluctuation-induced Casimir-like forces on the walls of the system are calculated assuming a fluctuating pressure tensor resulting from perturbing its Navier-Stokes expression. This way, the Casimir-like forces emerges as the correlation between the longitudinal velocity and the energy density. Interestingly, the fluctuation-induced forces push/pull the system towards the square or rectangular geometry when they vanish, in good agreement with the event-driven numerical simulations.
Polarization-induced stress in the noisy voter model
(Elsevier, 2024-05-20) Aguilar Janita, Miguel; Khalil, Nagi; Blanco Alonso, Andres
A new model for the dynamics of opinion formation is proposed and analysed at the mean-field level. It can be regarded as a generalization of the noisy voter model in which agents update their binary states by copying others and by an intrinsic mechanism affected by the degree of polarization in the system. It also takes into account whether the agents enhance or reduce their intrinsic mechanism upon increasing polarization. Four phases or shapes of the steady- state probability of a fraction of agents in a given state are found (unimodal, bimodal, W and M). In the unimodal (resp. bimodal) phase, the copying (resp. intrinsic) mechanism is globally dominant, while in the W (resp. M) phase the copying (resp. intrinsic) mechanism is the relevant one close to the consensus states while it reduces its influence as approaching coexistence. In the thermodynamic limit, the bimodal and W phases disappear, while the unimodal and M phases prevail. The theoretical results, obtained analytically from the master equation, and the numerical simulations are in good agreement.
Structured interactions as a stabilizing mechanism for competitive ecological communities
(2022) Calleja-Solanas, Violeta; Khalil, Nagi; Gómez-Gardeñes, Jesús; Hernández-Garcı́a, Emilio; Meloni, Sandro
How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open question in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and Physics. In this context, modeling the stable coexistence of different species competing for limited resources is a particularly demanding task. From the mathematical point of view, coexistence in competitive dynamics can be achieved when dominance among species forms intransitive loops. However, these relationships usually lead to species’ densities neutrally cycling without converging to a stable equilibrium and, although in recent years several mechanisms have been proposed, models able to explain the robust persistence of competitive ecosystems are lacking. Here we show that stable coexistence in large communities can be achieved when the locality of interactions is taken into account. We consider a simplified ecosystem where individuals of each species lay on a spatial network and interactions are possible only between nodes at a certain distance. Varying such distance allows to interpolate between local and global competition. Our results demonstrate that when two conditions are met: individuals are embedded in space and can only interact with other individuals within a short distance, species coexist reaching a stable equilibrium. On the contrary, when one of these ingredients is missing large fluctuations and neutral cycles emerge.