Related papers: Rock-scissors-paper game on regular small-world ne…
We study the oscillatory dynamics in the generic three-species rock-paper-scissors games with mutations. In the mean-field limit, different behaviors are found: (a) for high mutation rate, there is a stable interior fixed point with…
We study the cyclic dominance of three species in two-dimensional constrained Newman-Watts networks with a four-state variant of the rock-paper-scissors game. By limiting the maximal connection distance $R_{max}$ in Newman-Watts networks…
The rock-paper-scissors game is a paradigmatic model for biodiversity, with applications ranging from microbial populations to human societies. Research has shown, however, that mobility jeopardizes biodiversity by promoting the formation…
We study a stochastic lattice predator-prey system by means of Monte Carlo simulations that do not impose any restrictions on the number of particles per site, and discuss the similarities and differences of our results with those obtained…
A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow only two strategies: to cooperate (C) or to defect (D) unconditionally. The players updated in a random sequence have a…
Stochastic, spatially extended models for predator-prey interaction display spatio-temporal structures that are not captured by the Lotka-Volterra mean-field rate equations. These spreading activity fronts reflect persistent correlations…
The classic Rock-Paper-Scissors game of size 3 and its extension, Rock-Paper-Scissors-Lizard-Spock, are modeled by directed graphs called tournaments. They can be further extended to any odd size. The extended games are regular tournaments…
We investigate a modified spatial stochastic Lotka-Volterra formulation of the rock-paper-scissors model using off-lattice stochastic simulations. In this model one of the species moves preferentially in a specific direction -- the level of…
Spatial evolution is investigated in a simulated system of nine competing and mutating bacterium strains, which mimics the biochemical war among bacteria capable of producing two different bacteriocins (toxins) at most. Random sequential…
We consider an example of cyclic competition bimatrix game which is a Rock-Scissors-Paper game with assumption about perfect memory of the playing agents. At first we investigate the dynamics in the neighbourhood of the Nash equilibrium as…
The classical game of rock-paper-scissors have inspired experiments and spatial model systems that address robustness of biological diversity. In particular the game nicely illustrates that cyclic interactions allow multiple strategies to…
Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see e.g. B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature {\bf 418}, 171 (2002)] and B. Kirkup and M. A. Riley [Nature {\bf…
This work deals with the influence of the neighborhood in simple rock-paper-scissors models of biodiversity. We consider the case of three distinct species which evolve under the standard rules of mobility, reproduction and competition. The…
We model a situation in which a collection of species derive their fitnesses via a rock-paper-scissors-type game; however, the precise payoffs are a function of the environment. The new aspect of our model lies in adding a feedback loop:…
We study a five-species cyclic system wherein individuals of one species strategically adapt their movements to enhance their performance in the spatial rock-paper-scissors game. Environmental cues enable the awareness of the presence of…
When playing games in groups, it is an advantage for individuals to have accurate statistical information on the strategies of their opponents. Such information may be obtained by remembering previous interactions. We consider a…
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…
Rigidity percolation provides an important basis for understanding the onset of mechanical stability in disordered materials. While most studies on the triangular lattice have focused on static properties at fixed bond~(site) occupation…
Generalizing the cyclically competing three-species model (often referred to as the rock-paper-scissors game), we consider a simple system of population dynamics without spatial structures that involves four species. Unlike the previous…
Stochastic simulations of cyclic three-species spatial predator-prey models are usually performed in square lattices with nearest neighbor interactions starting from random initial conditions. In this Letter we describe the results of…