Rock is wrapped by paper, paper is cut by scissors and scissors are crushed by rock. This simple game is popular among children and adults to decide on trivial disputes that have no obvious winner, but cyclic dominance is also at the heart of predator–prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms and competition in microbial populations. Cyclical interactions also emerge spontaneously in evolutionary games entailing volunteering, reward, punishment, and in fact are common when the competing strategies are three or more, regardless of the particularities of the game. Here, we review recent advances on the rock–paper–scissors (RPS) and related evolutionary games, focusing, in particular, on pattern formation, the impact of mobility and the spontaneous emergence of cyclic dominance. We also review mean-field and zero-dimensional RPS models and the application of the complex Ginzburg–Landau equation, and we highlight the importance and usefulness of statistical physics for the successful study of large-scale ecological systems. Directions for future research, related, for example, to dynamical effects of coevolutionary rules and invasion reversals owing to multi-point interactions, are also outlined.

/pdf/cyclic-dominance-in-evolutionary-games-a-review-34pqhh53un.pdf

Cyclic dominance in evolutionary games: A review

https://cyberleninka.org/article/n/890491.pdf

Nanofluids for Solar Collector Applications: A Review

Rock is wrapped by paper, paper is cut by scissors, and scissors are crushed by rock. This simple game is popular among children and adults to decide on trivial disputes that have no obvious winner, but cyclic dominance is also at the heart of predator-prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms, and the competition in microbial populations. Cyclical interactions also emerge spontaneously in evolutionary games entailing volunteering, reward, punishment, and in fact are common when the competing strategies are three or more regardless of the particularities of the game. Here we review recent advances on the rock-paper-scissors and related evolutionary games, focusing in particular on pattern formation, the impact of mobility, and the spontaneous emergence of cyclic dominance. We also review mean-field and zero-dimensional rock-paper-scissors models and the application of the complex Ginzburg-Landau equation, and we highlight the importance and usefulness of statistical physics for the successful study of large-scale ecological systems. Directions for future research, related for example to dynamical effects of coevolutionary rules and invasion reversals due to multi-point interactions, are outlined as well.

We study a monomer-dimer model with repulsive interactions between the same species in one dimension. With infinitely strong interactions the model exhibits a continuous transition from a reactive phase to an inactive phase with two equivalent absorbing states. Monte Carlo simulations show that the critical behavior is different from the conventional directed percolation universality class but seems to be consistent with that of the models with the mass conservation of modulo 2.

Critical behavior of an interacting monomer-dimer model

A major hurdle in the simulation of the steady state of epidemic processes is that the system will unavoidably visit an absorbing, disease-free state at sufficiently long times due to the finite size of the networks where epidemics evolves. In the present work, we compare different quasistationary (QS) simulation methods where the absorbing states are suitably handled and the thermodynamical limit of the original dynamics can be achieved. We analyze the standard QS (SQS) method, where the sampling is constrained to active configurations, the reflecting boundary condition (RBC), where the dynamics returns to the pre-absorbing configuration, and hub reactivation (HR), where the most connected vertex of the network is reactivated after a visit to an absorbing state. We apply the methods to the contact process (CP) and susceptible-infected-susceptible (SIS) models on regular and scale free networks. The investigated methods yield the same epidemic threshold for both models. For CP, that undergoes a standard collective phase transition, the methods are equivalent. For SIS, whose phase transition is ruled by the hub mutual reactivation, the SQS and HR methods are able to capture localized epidemic phases while RBC is not. We also apply the autocorrelation time as a tool to characterize the phase transition and observe that this analysis provides the same finite-size scaling exponents for the critical relaxation time for the investigated methods. Finally, we verify the equivalence between RBC method and a weak external field for epidemics on networks.

/pdf/sampling-methods-for-the-quasistationary-regime-of-epidemic-47jm8wqv8t.pdf

Sampling methods for the quasistationary regime of epidemic processes on regular and complex networks

We study a spatial rock−scissors−paper model in a square lattice and a quenched small-world network. The system exhibits a global oscillation in the quenched small-world network, but the oscillation disappears in the square lattice. We find that there is a local oscillation in the square lattice the same as in the quenched small-world network. We define (where di is the density of a kind of species and di is the average value) as the variance of the oscillation amplitude in a certain local patch. It is found that s decays in a power law with an increase of the local patch size R in the square lattice σ ∝ R−δ, but it remains constant with an increase of the patch size in the quenched small-world network. We can speculate that in the square lattice, superposition between the local oscillations in different patches leads to global stabilization, while in the quenched small-world network, long-range interactions can synchronize the local oscillations, and their coherence results in the global oscillation.

http://iopscience.iop.org/article/10.1088/0256-307X/26/8/086403/pdf

Synchronization of Local Oscillations in a Spatial Rock?Scissors?Paper Game Model

The effect of the coadsorption of CO and O2 on the Ziff-Gulari-Barshad surface catalytic reaction system is studied by Monte Carlo simulation. The coadsorption of both species adds an extra reaction step to the classical Ziff-Gulari-Barshad model. It is shown that the second-order phase transition from the reactive state to the O-passivated state in the Ziff-Gulari-Barshad model is eliminated, and the production rate of CO2 increases linearly along the fraction yco of CO in gas phase when it is low, in agreement with experimental results. We also find that the increase of the probability of the coadsorption leads to the decrease of the critical value of yco of the discontinuous phase transition to the CO-passivated state.

Effect of the Coadsorption of CO and O 2 on the Phase Diagram of the Ziff-Gulari-Barshad Model

We investigate the dynamical behaviour of the aggregation process in the symmetric conserved mass aggregation model under three different topological structures. The dispersion σ(t, L) = (σi(mi – ρ0)2/L)½ is defined to describe the dynamical behaviour where ρo is the density of particle and mi is the particle number on a site. It is found numerically that for a regular lattice and a scale-free network, σ(t, L) follows a power-law scaling σ(t, L) ~ tδ1 and σ(t, L) ~ δ4 from a random initial condition to the stationary states, respectively. However, for a small-world network, there are two power-law scaling regimes, σ(t, L) ~ tδ2 when t T. Moreover, it is found numerically that δ2 is near to δ1 for small rewiring probability q, and δ3 hardly changes with varying q and it is almost the same as δ4. We speculate that the aggregation of the connection degree accelerates the mass aggregation in the initial relaxation stage and the existence of the long-distance interactions in the complex networks results in the acceleration of the mass aggregation when t > T for the small-world networks. We also show that the relaxation time τ follows a power-law scaling τ ~ Lz and σ(t, T) in the stationary state follows a power-law σs(L) ~ Lα for three different structures.

Dynamics of Symmetric Conserved Mass Aggregation Model on Complex Networks

We investigate the phase transition of the pair contact process (PCP) model in a fragmented network. The network is formed by rewiring the link between two nearest neighbors to another randomly selected site in one dimension with a probability q. When the average degree (k) = 2, the system exhibits a structure transition and the lattice is fragmented into several isolated subgraphs, it is shown that a giant cluster appears and its node fraction does not change nearly for q > 0. Furthermore, it is found that the critical behavior of the continuous phase transition for the PCP model is different from the directed percolation (DP) class and the estimated values of the critical exponents are independent of the rewiring probability for q > 0. We conjecture that the structure transition for (k) = 2 takes an important role in the change of the critical behavior of the continuous phase transition.

Phase Transition of the Pair Contact Process Model in a Fragmented Network

We studied the effect of population density in a spatial public goods game. We found that the effect on the evolution of cooperation is very complex when the strategy learning and mobility of players in a long range are considered in a two-dimensional lattice. As the learning range is larger than the mobility range, the system is driven to enter into a cooperation state for a low population density, because a small local group is beneficial to sustain a high level of cooperation. As population density increases to a moderate range, the mobility of players from a domain invaded by defectors supports the evolution stability of cooperation. When the mobility range is larger than the learning range, a formation of compact domains of cooperators promotes cooperation as the population density becomes high.

Hua Da-Yin

Papers

Synchronization of Local Oscillations in a Spatial Rock?Scissors?Paper Game Model

Effect of the Coadsorption of CO and O 2 on the Phase Diagram of the Ziff-Gulari-Barshad Model

Dynamics of Symmetric Conserved Mass Aggregation Model on Complex Networks

Phase Transition of the Pair Contact Process Model in a Fragmented Network

Promotion of Cooperation in a Spatial Public Goods Game with Long Range Learning and Mobility