Biomedical subjects

Attila Szolnoki

Publications and source records attributed to Attila Szolnoki.

10 recordsLinked to original sources

PubMed2006

Cooperation in the 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 noise the optimal connectivity structure is built up from randomly connected triangles.

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PubMed2005

Phase diagrams for an evolutionary 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 Monte Carlo simulations and 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 the cooperation can be sustained only for those connectivity structures where three-site clique percolation occurs.

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PubMed2005

Cluster mean-field study of the parity-conserving phase transition.

The phase transition of the branching and annihilating random walk with even offspring is studied by N-cluster mean-field approximations on one-dimensional lattices. By allowing the system to reach zero branching rate a phase transition can be seen for any N < or = 12. Coherent anomaly extrapolations applied for the series of approximations results in nu(perpendicular) = 1.85(3) and beta=0.96(2).

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PubMed2005

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 exemplified in the rock-scissors-paper game. Monte Carlo simulations are performed on a square lattice while 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, which yields a self-organizing pattern even at low temperatures. The differences and similarities are discussed between the present model and half-filled, driven lattice gases with repulsive interaction.

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PubMed2004

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 the 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 the 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.

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PubMed2004

Vertex dynamics during domain growth in three-state models.

Topological aspects of interfaces are studied by comparing quantitatively the evolving three-color patterns in three different models, such as the three-state voter, Potts, and extended voter models. The statistical analysis of some geometrical features allows us to explore the role of different elementary processes during distinct coarsening phenomena in the above models.

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PubMed2004

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 exhibits 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.

Animals↗

PubMed2002

Dynamical mean-field approximation for a 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>or=6 and allow us to derive reliable extrapolations to the limit n--> infinity. At the zero source limit, the critical point exhibits a discontinuity whose magnitude vanishes with 1/n. Coherent anomaly analysis of the data supports the conclusion that the vanishing of the order parameter and the density of isolated particles have 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.

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PubMed2002

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 the phase diagram are reproduced by an improved mean-field analysis.

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PubMed2002

Three-state cyclic voter model extended with Potts energy.

The cyclically dominated voter model on a square is extended by taking into consideration the variation of Potts energy during the nearest neighbor invasions. We have investigated the effect of surface tension on the self-organizing patterns maintained by the cyclic invasions. A geometrical analysis is also developed to study the three-color patterns. These investigations clearly indicate that in the "voter model" limit the pattern evolution is governed by the loop creation due to the overhanging during the interfacial roughening. Conversely, in the presence of surface tension the evolution is governed by spiral formation whose geometrical parameters depend on the strength of cyclic dominance.

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