arXiv subjects

Gyorgy Szabo

Publications and source records attributed to Gyorgy Szabo.

At least 37 records · Page 2Linked to original sources

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↗

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

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.

cond-mat.stat-mech↗

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↗

arXiv2005

Competing associations in six-species predator-prey models

We study a set of six-species ecological models where each species has two predators and two preys. On a square lattice the time evolution is governed by iterated invasions between the neighboring predator-prey pairs chosen at random and by a site exchange with a probability Xs between the neutral pairs. These models involve the possibility of spontaneous formation of different defensive alliances whose members protect each other from the external invaders. The Monte Carlo simulations show a surprisingly rich variety of the stable spatial distributions of species and subsequent phase transitions when tuning the control parameter Xs. These very simple models are able to demonstrate that the competition between these associations influences their composition. Sometimes the dominant association is developed via a domain growth. In other cases larger and larger invasion processes preceed the prevalence of one of the stable asociations. Under some conditions the survival of all the species can be maintained by the cyclic dominance occuring between these associations.

q-bio.PE↗

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

Evolutionary prisoner's dilemma game on hierarchical lattices

An evolutionary prisoner's dilemma (PD) game is studied with players located on a hierarchical structure of layered square lattices. The players can follow two strategies [D (defector) and C (cooperator)] and their income comes from PD games with the ``neighbors.'' The adoption of one of the neighboring strategies is allowed with a probability dependent on the payoff difference. Monte Carlo simulations are performed to study how the measure of cooperation is affected by the number of hierarchical levels (Q) and by the temptation to defect. According to the simulations the highest frequency of cooperation can be observed at the top level if the number of hierarchical levels is low (Q<4). For larger Q, however, the highest frequency of cooperators occurs in the middle layers. The four-level hierarchical structure provides the highest average (total) income for the whole community.

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↗

arXiv2003

Phase transition and selection in a four-species cyclic Lotka-Volterra model

We study a four species ecological system with cyclic dominance whose individuals are distributed on a square lattice. Randomly chosen individuals migrate to one of the neighboring sites if it is empty or invade this site if occupied by their prey. The cyclic dominance maintains the coexistence of all the four species if the concentration of vacant sites is lower than a threshold value. Above the treshold, a symmetry breaking ordering occurs via growing domains containing only two neutral species inside. These two neutral species can protect each other from the external invaders (predators) and extend their common territory. According to our Monte Carlo simulations the observed phase transition is equivalent to those found in spreading models with two equivalent absorbing states although the present model has continuous sets of absorbing states with different portions of the two neutral species. The selection mechanism yielding symmetric phases is related to the domain growth process whith wide boundaries where the four species coexist.

q-bio.PE↗

arXiv2002

Evolutionary prisoner's dilemma games with optional participation

Competition among cooperators, defectors, and loners is studied in an evolutionary prisoner's dilemma game with optional participation. Loners are risk averse i.e. unwilling to participate and rather rely on small but fixed earnings. This results in a rock-scissors-paper type cyclic dominance of the three strategies. The players are located either on square lattices or random regular graphs with the same connectivity. Occasionally, every player reassesses its strategy by sampling the payoffs in its neighborhood. The loner strategy efficiently prevents successful spreading of selfish, defective behavior and avoids deadlocks in states of mutual defection. On square lattices, Monte Carlo simulations reveal self-organizing patterns driven by the cyclic dominance, whereas on random regular graphs different types of oscillatory behavior are observed: the temptation to defect determines whether damped, periodic or increasing oscillations occur. These results are compared to predictions by pair approximation. Although pair approximation is incapable of distinguishing the two scenarios because of the equal connectivity, the average frequencies as well as the oscillations on random regular graphs are well reproduced.

cond-mat.dis-nn↗

arXiv2002

Phase transitions and volunteering in spatial public goods games

Cooperative behavior among unrelated individuals in human and animal societies represents a most intriguing puzzle to scientists in various disciplines. Here we present a simple yet effective mechanism promoting cooperation under full anonymity by allowing for voluntary participation in public goods games. This natural extension leads to rock--scissors--paper type cyclic dominance of the three strategies cooperate, defect and loner i.e. those unwilling to participate in the public enterprise. In spatial settings with players arranged on a regular lattice this results in interesting dynamical properties and intriguing spatio-temporal patterns. In particular, variations of the value of the public good leads to transitions between one-, two- and three-strategy states which are either in the class of directed percolation or show interesting analogies to Ising-type models. Although volunteering is incapable of stabilizing cooperation, it efficiently prevents successful spreading of selfish behavior and enables cooperators to persist at substantial levels.

cond-mat↗

arXiv2002

On the Role of External Constraints in a Spatially Extended Evolutionary Prisoner's Dilemma Game

We study the emergency of mutual cooperation in evolutionary prisoner's dilemma games when the players are located on a square lattice. The players can choose one of the three strategies: cooperation (C), defection (D) or "tit for tat" (T), and their total payoffs come from games with the nearest neighbors. During the random sequential updates the players adopt one of their neighboring strategies if the chosen neighbor has higher payoff. We compare the effect of two types of external constraints added to the Darwinian evolutionary processes. In both cases the strategy of a randomly chosen player is replaced with probability P by another strategy. In the first case, the strategy is replaced by a randomly chosen one among the two others, while in the second case the new strategy is always C. Using generalized mean-field approximations and Monte Carlo simulations the strategy concentrations are evaluated in the stationary state for different strength of external constraints characterized by the probability P.

cond-mat.stat-mech↗

arXiv2002

Generalized contact process on random environments

Spreading from a seed is studied by Monte Carlo simulation on a square lattice with two types of sites affecting the rates of birth and death. These systems exhibit a critical transition between survival and extinction. For time- dependent background, this transition is equivalent to those found in homogeneous systems (i.e. to directed percolation). For frozen backgrounds, the appearance of Griffiths phase prevents the accurate analysis of this transition. For long times in the subcritical region, spreading remains localized in compact (rather than ramified) patches, and the average number of occupied sites increases logarithmically in the surviving trials.

cond-mat.dis-nn↗

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↗