arXiv subjects

Attila Szolnoki

Publications and source records attributed to Attila Szolnoki.

At least 181 records · Page 10Linked to original sources

arXiv2008

Evolutionary Prisoner's Dilemma game on the Newman-Watts networks

Maintenance of cooperation was studied for a two-strategy evolutionary Prisoner's Dilemma game where the players are located on a one-dimensional chain and their payoff comes from games with the nearest and next-nearest neighbor interactions. The applied host geometry makes possible to study the impacts of two conflicting topological features. The evolutionary rule involves some noise affecting the strategy adoptions between the interacting players. Using Monte Carlo simulations and the extended versions of dynamical mean-field theory we determined the phase diagram as a function of noise level and a payoff parameter. The peculiar feature of the diagram is changed significantly when the connectivity structure is extended by extra links as suggested by Newman and Watts.

physics.soc-ph↗

arXiv2008

Phase transitions induced by variation of invasion rates in spatial cyclic predator-prey models with four or six species

Cyclic predator-prey models with four or six species are studied on a square lattice when the invasion rates are varied. It is found that the cyclic invasions maintain a self-organizing pattern as long as the deviation of the invasion rate(s) from a uniform value does not exceed a threshold value. For larger deviations the system exhibits a continuous phase transition into a frozen distribution of odd (or even) label species.

q-bio.PE↗

arXiv2008

Social diversity and promotion of cooperation in the spatial prisoner's dilemma game

The diversity in wealth and social status is present not only among humans, but throughout the animal world. We account for this observation by generating random variables that determ ine the social diversity of players engaging in the prisoner's dilemma game. Here the term social diversity is used to address extrinsic factors that determine the mapping of game pay offs to individual fitness. These factors may increase or decrease the fitness of a player depending on its location on the spatial grid. We consider different distributions of extrin sic factors that determine the social diversity of players, and find that the power-law distribution enables the best promotion of cooperation. The facilitation of the cooperative str ategy relies mostly on the inhomogeneous social state of players, resulting in the formation of cooperative clusters which are ruled by socially high-ranking players that are able to prevail against the defectors even when there is a large temptation to defect. To confirm this, we also study the impact of spatially correlated social diversity and find that coopera tion deteriorates as the spatial correlation length increases. Our results suggest that the distribution of wealth and social status might have played a crucial role by the evolution of cooperation amongst egoistic individuals.

physics.soc-ph↗

arXiv2007

Towards effective payoffs in the prisoner's dilemma game on scale-free networks

We study the transition towards effective payoffs in the prisoner's dilemma game on scale-free networks by introducing a normalization parameter guiding the system from accumulated payoffs to payoffs normalized with the connectivity of each agent. We show that during this transition the heterogeneity-based ability of scale-free networks to facilitate cooperative behavior deteriorates continuously, eventually collapsing with the results obtained on regular graphs. The strategy donations and adaptation probabilities of agents with different connectivities are studied. Results reveal that strategies generally spread from agents with larger towards agents with smaller degree. However, this strategy adoption flow reverses sharply in the fully normalized payoff limit. Surprisingly, cooperators occupy the hubs even if the averaged cooperation level due to partly normalized payoffs is moderate.

physics.bio-ph↗

arXiv2007

Segregation process and phase transition in cyclic predator-prey models with even number of species

We study a spatial cyclic predator-prey model with an even number of species (for n=4, 6, and 8) that allows the formation of two defective alliances consisting of the even and odd label species. The species are distributed on the sites of a square lattice. The evolution of spatial distribution is governed by iteration of two elementary processes on neighboring sites chosen randomly: if the sites are occupied by a predator-prey pair then the predator invades the prey's site; otherwise the species exchange their site with a probability $X$. For low $X$ values a self-organizing pattern is maintained by cyclic invasions. If $X$ exceeds a threshold value then two types of domains grow up that formed by the odd and even label species, respectively. Monte Carlo simulations indicate the blocking of this segregation process within a range of X for n=8.

physics.bio-ph↗

arXiv2007

Noise-guided evolution within cyclical interactions

We study a stochastic predator-prey model on a square lattice, where each of the six species has two superior and two inferior partners. The invasion probabilities between species depend on the predator-prey pair and are supplemented by Gaussian noise. Conditions are identified that warrant the largest impact of noise on the evolutionary process, and the results of Monte Carlo simulations are qualitatively reproduced by a four-point cluster dynamical mean-field approximation. The observed noise-guided evolution is deeply routed in short-range spatial correlations, which is supported by simulations on other host lattice topologies. Our findings are conceptually related to the coherence resonance phenomenon in dynamical systems via the mechanism of threshold duality. We also show that the introduced concept of noise-guided evolution via the exploitation of threshold duality is not limited to predator-prey cyclical interactions, but may apply to models of evolutionary game theory as well, thus indicating its applicability in several different fields of research.

q-bio.PE↗

arXiv2007

Cyclical interactions with alliance-specific heterogeneous invasion rates

We study a six-species Lotka-Volterra type system on different two-dimensional lattices when each species has two superior and two inferior partners. The invasion rates from predator sites to a randomly chosen neighboring prey's site depend on the predator-prey pair, whereby cyclic symmetries within the two three-species defensive alliances are conserved. Monte Carlo simulations reveal an unexpected non-monotonous dependence of alliance survival on the difference of alliance-specific invasion rates. This behavior is qualitatively reproduced by a four-point mean-field approximation. The study addresses fundamental problems of stability for the competition of two defensive alliances and thus has important implications in natural and social sciences.

cond-mat.stat-mech↗

arXiv2006

Cooperation enhanced by inhomogeneous activity of teaching for evolutionary Prisoner's Dilemma games

Evolutionary Prisoner's Dilemma games with quenched inhomogeneities in the spatial dynamical rules are considered. The players following one of the two pure strategies (cooperation or defection) are distributed on a two-dimensional lattice. The rate of strategy adoption from a randomly chosen neighbors are controlled by the payoff difference and a two-value pre-factor $w$ characterizing the players whom the strategy learned from. The reduced teaching activity of players is distributed randomly with concentrations $ν$ at the beginning and fixed further on. Numerical and analytical calculations are performed to study the concentration of cooperators as a function of $w$ and $ν$ for different noise levels and connectivity structures. Significant increase of cooperation is found within a wide range of parameters for this dynamics. The results highlight the importance of asymmetry characterizing the exchange of master-follower role during the strategy adoptions.

q-bio.PE↗

arXiv2006

Cooperation in noisy case: prisoner's dilemma game on two types of regular random graphs

We have studied an evolutionary prisoner's dilemma game with players located on two types of random regular graphs with a degree of 4. The analysis is focused on the effects of payoffs and noise (temperature) on the maintenance of cooperation. When varying the noise level and/or the highest payoff, the system exhibits a second order phase transition from a mixed state of cooperators and defectors to an absorbing state where only defectors remain alive. For the random regular graph (and Bethe lattice) the behavior of the system is similar to those found previously on the square lattice with nearest neighbor interactions, although the measure of cooperation is enhanced by the absence of loops in the connectivity structure. For low noises the optimal connectivity structure is built up from randomly connected triangles.

cond-mat.stat-mech↗

arXiv2005

Phase diagrams for Prisoner's Dilemma game on two-dimensional lattices

The effects of payoffs and noise on the maintenance of cooperative behavior are studied in an evolutionary Prisoner's Dilemma game with players located on the sites of different two-dimensional lattices. This system exhibits a phase transition from a mixed state of cooperators and defectors to a homogeneous one where only the defectors remain alive. Using systematic Monte Carlo simulations and different levels of the generalized mean-field approximations we have determined the phase boundaries (critical points) separating the two phases on the plane of the temperature (noise) and temptation to choose defection. In the zero temperature limit this analysis suggests that the cooperation can be sustained only for those connectivity structures where three-site clique percolation occurs.

cond-mat.stat-mech↗

arXiv2005

Cluster mean-field study of the parity conserving phase transition

The phase transition of the even offspringed branching and annihilating random walk is studied by N-cluster mean-field approximations on one-dimensional lattices. By allowing to reach zero branching rate a phase transition can be seen for any N <= 12.The coherent anomaly extrapolations applied for the series of approximations results in $ν_{\perp}=1.85(3)$ and $β=0.96(2)$.

cond-mat.stat-mech↗

arXiv2004

Dynamical mean-field approximations for a diffusive pair contact process

Dynamical mean-field approximations are performed to study the phase transition of a pair contact process with diffusion in different spatial dimensions. The level of approximation is extended up to 18-site clusters for the one-dimensional model. The application of coherent anomaly method shows that the critical $β$ exponent does not depend on the strength of diffusion rate. The extension of the mean-field approximation to higher dimensions also suggests that the critical behavior may be described by a unique set of exponents.

cond-mat.stat-mech↗

arXiv2004

Phase transitions for rock-scissors-paper game on different networks

Monte Carlo simulations and dynamical mean-field approximations are performed to study the phase transitions in rock-scissors-paper game on different host networks. These graphs are originated from lattices by introducing quenched and annealed randomness simultaneously. In the resulting phase diagrams three different stationary states are identified for all structures. The comparison of results on different networks suggests that the value of clustering coefficient plays an irrelevant role in the emergence of a global oscillating phase. The critical behavior of phase transitions seems to be universal and can be described by the same exponents.

cond-mat.stat-mech↗

arXiv2004

Three-state Potts model in combination with the rock-scissors-paper game

We study a three-state Potts model extended by allowing cyclic dominance between the states as it appears for the rock-scissors-paper game. Monte Carlo simulations are performed on a square lattice when varying the temperature and the strength of cyclic dominance. It is shown that the critical phase transition from the disordered state to the ordered one is destroyed by the cyclic dominance that yields a self-organizing pattern even at low temperatures. The differences and similarities are discussed between the present model and the half-filled, driven lattice gases with repulsive interaction.

cond-mat.stat-mech↗

arXiv2004

Spreading of families in cyclic predator-prey models

We study the spreading of families in two-dimensional multispecies predator-prey systems, in which species cyclically dominate each other. In each time step randomly chosen individuals invade one of the nearest sites of the square lattice eliminating their prey. Initially all individuals get a family-name which will be carried on by their descendants. Monte Carlo simulations show that the systems with several species (N=3,4,5) are asymptotically approaching the behavior of the voter model, i.e., the survival probability of families, the mean-size of families and the mean-square distance of descendants from their ancestor exhibit the same scaling behavior. The scaling behavior of the survival probability of families has a logarithmic correction. In case of the voter model this correction depends on the number of species, while cyclic predator-prey models behave like the voter model with infinite species. It is found that changing the rates of invasions does not change this asymptotic behavior. As an application a three-species system with a fourth species intruder is also discussed.

q-bio.PE↗

arXiv2004

Rock-scissors-paper game on regular small-world networks

The spatial rock-scissors-paper game (or cyclic Lotka-Volterra system) is extended to study how the spatiotemporal patterns are affected by the constructed backgrounds providing uniform number of neighbors (degree) at each site. On the square lattice this system exhibits a self-organizing pattern with equal concentration of the competing strategies (species). If the quenched background is constructed by substituting random links for the nearest neighbor bonds of a square lattice then a limit cycle occurs when the portion of random links exceeds a threshold value. This transition can also be observed if the standard link is replaced temporarily by a random one with a probability $P$ at each step of iteration. Above a second threshold value of $P$ the amplitude of global oscillation increases with time and finally the system reaches one of the homogeneous (absorbing) states. In this case the results of Monte Carlo simulations are compared with the predictions of the dynamical cluster technique evaluating all the configuration probabilities on one-, two-, four-, and six-site clusters.

cond-mat.stat-mech↗

arXiv2002

Dynamical mean-field approximation for pair contact process with a particle source

The one-dimensional pair contact process with a particle source is studied by using dynamical cluster mean-field approximations with sites up to $n=12$. The results obtained for different levels of approximation become convergent especially for $n \ge 6$ and allow us to derive reliable extrapolations to the limit $n \to \infty$. At the zero source limit, the critical point exhibits a discontinuity whose magnitude vanishes with $1/n$. The coherent anomaly analysis of data supports that the vanishing of order parameter and density of isolated particles has the same critical behavior. In contrast to an earlier prediction, the present approximation does not support the existence of critical behavior in the inactive phase where the frozen density of isolated particles depends on the initial state.

cond-mat.stat-mech↗

arXiv2001

Influence of extended dynamics on phase transitions in a driven lattice gas

Monte Carlo simulations and dynamical mean-field approximations are performed to study the phase transition in a driven lattice gas with nearest-neighbor exclusion on a square lattice. A slight extension of the microscopic dynamics with allowing the next-nearest-neighbor hops results in dramatic changes. Instead of the phase separation into high- and low-density regions in the stationary state the system exhibits a continuous transition belonging to the Ising universality class for any driving. The relevant features of phase diagram are reproduced by an improved mean-field analysis.

cond-mat.stat-mech↗