Related papers: Mean extinction times in cyclic coevolutionary roc…
We study the spatial rock-paper-scissors model, where resource competitors' cyclic dominance impacts organisms' energy levels. Our model assumes that failed selection interactions can lead to energy loss, reducing the chances of success in…
Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic…
Rock-Paper-Scissors (RPS), a game of cyclic dominance, is not merely a popular children's game but also a basic model system for studying decision-making in non-cooperative strategic interactions. Aimed at students of physics with no…
We study a generalized discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic…
We study generalised rock-paper-scissors models with an arbitrary odd number N \geq 5 of species, among which n are weak, with 2 \leq n \leq (N-1)/2. Because of the species' weakness, the probability of individuals conquering territory in…
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:…
When microbes compete for limited resources, they often engage in chemical warfare using bacterial toxins. This competition can be understood in terms of evolutionary game theory (EGT). We study the predictions of EGT for the bacterial…
As the behavior of a system composed of cyclically competing species is strongly influenced by the presence of fluctuations, it is of interest to study cyclic dominance in low dimensions where these effects are the most prominent. We here…
We study several variants of the stochastic four-state rock-paper-scissors game or, equivalently, cyclic three-species predator-prey models with conserved total particle density, by means of Monte Carlo simulations on one- and…
We investigate a tritrophic system whose cyclic dominance is modelled by the rock-paper-scissors game. We consider that organisms of one or two species are affected by movement limitations, which unbalances the cyclic spatial game.…
How humans make decisions in non-cooperative strategic interactions is a challenging question. For the fundamental model system of Rock-Paper-Scissors (RPS) game, classic game theory of infinite rationality predicts the Nash equilibrium…
The rock-paper-scissors game is a model example of the on-going cyclic turnover typical of many ecosystems, ranging from the terrestrial and aquatic to the microbial. Here we explore the evolution of a rock-paper-scissors system where three…
A cyclically dominating three-species ecosystem, modeled within the framework of rock-paper-scissor game, is studied in presence of natural death and an effect of the environment. The environmental impact is parameterized along with the…
In the May-Leonard model of three cyclically competing species, we analyze the statistics of rare events in which all three species go extinct due to strong but rare fluctuations. These fluctuations are from the tails of the probability…
Climate changes may affect ecosystems destabilising relationships among species. We investigate the spatial rock-paper-scissors models with a regional unevenness that reduces the selection capacity of organisms of one species. Our results…
We study the influence of a randomly switching reproduction-predation rate on the survival behavior of the non-spatial cyclic Lotka-Volterra model, also known as the zero-sum rock-paper-scissors game, used to metaphorically describe the…
The Rock-Paper-Scissors (RPS) game and its generalizations with ${\cal S}>3$ species are well studied models for cyclically interacting populations. Four is, however, the minimum number of species that, by allowing other interactions beyond…
In this paper we compute the stopping times in the game Rock-Paper-Scissors. By exploiting the recurrence relation we compute the mean values of stopping times. On the other hand, by constructing a transition matrix for a Markov chain…
Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra…
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…