arXiv subjects

Guillermo Abramson

Publications and source records attributed to Guillermo Abramson.

At least 37 records · Page 2Linked to original sources

arXiv2013

Imitation dynamics in a game of traffic

We study a model of traffic where drivers adopt different behavioral strategies. These can be cooperative or defective according to a driver abiding or not by a traffic rule. Drivers can change their strategy by imitating the majority, with a rule that depends on the strategies with which they have interacted. These interactions occur at intersections, where vehicles pay a temporal cost according to their strategy. We analyze the conditions under which different strategy compositions represent an advantage in the system velocity. We found that the cooperators' mean speed is higher than the defectors' even when the vehicle density is large. However, defectors can obtain benefits in their mean speed when they are a minority in an essentially cooperative population. The presence of a core of educated drivers, who persist firmly in a cooperative behavior, optimizes the speed in the system, especially for intermediate values of vehicular density and higher temporal costs.

nlin.AO↗

arXiv2010

The role of asymmetric interactions on the effect of habitat destruction in mutualistic networks

Plant-pollinator mutualistic networks are asymmetric in their interactions: specialist plants are pollinated by generalist animals, while generalist plants are pollinated by a broad involving specialists and generalists. It has been suggested that this asymmetric ---or disassortative--- assemblage could play an important role in determining the equal susceptibility of specialist and generalist plants under habitat destruction. At the core of the argument lies the observation that specialist plants, otherwise candidates to extinction, could cope with the disruption thanks to their interaction with generalist pollinators. We present a theoretical framework that supports this thesis. We analyze a dynamical model of a system of mutualistic plants and pollinators, subject to the destruction of their habitat. We analyze and compare two families of interaction topologies, ranging from highly assortative to highly disassortative ones, as well as real pollination networks. We found that several features observed in natural systems are predicted by the mathematical model. First, there is a tendency to increase the asymmetry of the network as a result of the extinctions. Second, an entropy measure of the differential susceptibility to extinction of specialist and generalist species show that they tend to balance when the network is disassortative. Finally, the disappearance of links in the network, as a result of extinctions, shows that specialist plants preserve more connections than the corresponding plants in an assortative system, enabling them to resist the disruption.

q-bio.PE↗

arXiv2007

Oscillations in two-species models: tying the stochastic and deterministic approaches

We analyze general two-species stochastic models, of the kind generally used for the study of population dynamics. We show that the conditions for the stochastic (microscopic) model to display approximate sustained oscillatory behavior are governed by the parameters of the corresponding deterministic (macroscopic) model. We provide a quantitative criterion for the quality of the stochastic oscillation, using a dimensionless parameter that depends only on the deterministic model. When this parameter is small, the oscillations are clear, and the frequencies of the stochastic and deterministic oscillations are close, for all stochastic models compatible with the same deterministic one. On the other hand, when it is large, the oscillations cannot be distinguished from a noise.

q-bio.PE↗

arXiv2005

The effect of biodiversity on the Hantavirus epizootic

We analyze a mathematical model of the epizootic of Hantavirus in mice population, including the effect of species which compete with the host. We show that the existence of the second species has an important consequence for the prevalence of the infectious agent in the host. When the two mice species survive in the ecosystem, the competitive pressure of the second species may lead to reduction or complete elimination of the prevalence of infection. The transition between the disappearance of the infection and its presence occurs at a critical value of the competitor's population, resembling a second order phase transition in a statistical system. The results provide a rigorous framework for the study of the impact of biodiversity in the propagation of infectious diseases, and further lends itself to future experimental verification.

q-bio.PE↗

arXiv2004

The criticality of the Hantavirus infected phase at Zuni

A preliminary analysis of the temporal evolution of a population of \emph{Peromyscus maniculatus} infected with Hantavirus Sin Nombre is made. Ecological and epidemiological parameters are derived from the data, and they are used as inputs for the analytical model presented in [Abramson and Kenkre, Phys. Rev. E \textbf{66}, 011912 (2002)]. A prediction of the critical carrying capacity and its associated critical mouse density is made, and the time series is analyzed under the light of these. It is found that the sporadic disappearances and reappearances of the infected phase correspond to the bifurcation predicted by the model.

q-bio.PE↗

arXiv2003

Associative memory on a small-world neural network

We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered networks are unable to recover the patterns, and are always attracted to mixture states. Besides, for a range of the number of stored patterns, the efficacy has a maximum at an intermediate value of the disorder. We also give a statistical characterization of the attractors for all values of the disorder of the network.

nlin.AO↗

arXiv2003

Minorities in a model for opinion formation

We study a model for social influence in which the agents' opinion is a continuous variable [G. Weisbuch et al., Complexity \textbf{7}, 2, 55 (2002)]. The convergent opinion adjustment process takes place as a result of random binary encounters whenever the difference between agents' opinions is below a given threshold. The inhomogeneity in the dynamics gives rise to a complex steady state structure, which is also highly dependent on the threshold and on the convergence parameter of the model.

cond-mat.stat-mech↗

arXiv2003

Vector opinion dynamics in a model for social influence

We present numerical simulations of a model of social influence, where the opinion of each agent is represented by a binary vector. Agents adjust their opinions as a result of random encounters, whenever the difference between opinions is below a given threshold. Evolution leads to a steady state, which highly depends on the threshold and a convergence parameter of the model. We analyze the transition between clustered and homogeneous steady states. Results of the cases of complete mixing and small-world networks are compared.

cond-mat.stat-mech↗

arXiv2002

Two-dimensional projections of an hypercube

We present a method to project a hypercube of arbitrary dimension on the plane, in such a way as to preserve, as well as possible, the distribution of distances between vertices. The method relies on a Montecarlo optimization procedure that minimizes the squared difference between distances in the plane and in the hypercube, appropriately weighted. The plane projections provide a convenient way of visualization for dynamical processes taking place on the hypercube.

physics.comp-ph↗

arXiv2001

Effects of Transport Memory and Nonlinear Damping in a Generalized Fisher's Equation

Memory effects in transport require, for their incorporation into reaction diffusion investigations, a generalization of traditional equations. The well-known Fisher's equation, which combines diffusion with a logistic nonlinearity, is generalized to include memory effects and traveling wave solutions of the equation are found. Comparison is made with alternate generalization procedures.

nlin.PS↗

arXiv2001

Complex structures in generalized small worlds

We propose a generalization of small world networks, in which the reconnection of links is governed by a function that depends on the distance between the elements to be linked. An adequate choice of this function lets us control the clusterization of the system. Control of the clusterization, in turn, allows the generation of a wide variety of topologies.

nlin.AO↗

arXiv2000

Long transients and cluster size in globally coupled maps

We analyze the asymptotic states in the partially ordered phase of a system of globally coupled logistic maps. We confirm that, regardless of initial conditions, these states consist of a few clusters, and they properly belong in the ordered phase of these systems. The transient times necessary to reach the asymptotic states can be very long, especially very near the transition line separating the ordered and the coherent phases. We find that, where two clusters form, the distribution of their sizes corresponds to windows of regular or narrow-band chaotic behavior in the bifurcation diagram of a system of two degrees of freedom that describes the motion of two clusters, where the size of one cluster acts as a bifurcation parameter.

nlin.AO↗

arXiv2000

Social games in a social network

We study an evolutionary version of the Prisoner's Dilemma game, played by agents placed in a small-world network. Agents are able to change their strategy, imitating that of the most successful neighbor. We observe that different topologies, ranging from regular lattices to random graphs, produce a variety of emergent behaviors. This is a contribution towards the study of social phenomena and transitions governed by the topology of the community.

nlin.AO↗

arXiv2000

Small world effect in an epidemiological model

A model for the spread of an infection is analyzed for different population structures. The interactions within the population are described by small world networks, ranging from ordered lattices to random graphs. For the more ordered systems, there is a fluctuating endemic state of low infection. At a finite value of the disorder of the network, we find a transition to self-sustained oscillations in the size of the infected subpopulation.

nlin.AO↗

arXiv2000

Synchronization learning of coupled chaotic maps

We study the dynamics of an ensemble of globally coupled chaotic logistic maps under the action of a learning algorithm aimed at driving the system from incoherent collective evolution to a state of spontaneous full synchronization. Numerical calculations reveal a sharp transition between regimes of unsuccessful and successful learning as the algorithm stiffness grows. In the regime of successful learning, an optimal value of the stiffness is found for which the learning time is minimal.

nlin.AO↗

arXiv1999

Extremal Coupled Map Lattices

We propose a model for co-evolving ecosystems that takes into account two levels of description of an organism, for instance genotype and phenotype. Performance at the macroscopic level forces mutations at the microscopic level. These, in turn, affect the dynamics of the macroscopic variables. In some regions of parameter space, the system self-organises into a state with localised activity and power law distributions.

adap-org↗

arXiv1998

Statistics of extinction and survival in Lotka-Volterra systems

We analyze purely competitive many-species Lotka-Volterra systems with random interaction matrices, focusing the attention on statistical properties of their asymptotic states. Generic features of the evolution are outlined from a semiquantitative analysis of the phase-space structure, and extensive numerical simulations are performed to study the statistics of the extinctions. We find that the number of surviving species depends strongly on the statistical properties of the interaction matrix, and that the probability of survival is weakly correlated to specific initial conditions.

adap-org↗

arXiv1998

Globally coupled maps with asynchronous updating

We analyze a system of globally coupled logistic maps with asynchronous updating. We show that its dynamics differs considerably from that of the synchronous case. For growing values of the coupling intensity, an inverse bifurcation cascade replaces the structure of clusters and ordering in the phase diagram. We present numerical simulations and an analytical description based on an effective single-element dynamics affected by internal fluctuations. Both of them show how global coupling is able to suppress the complexity of the single-element evolution. We find that, in contrast to systems with synchronous update, internal fluctuations satisfy the law of large numbers.

chao-dyn↗