Related papers: Junctions and spiral patterns in Rock-Paper-Scisso…
Rock-paper-scissors games metaphorically model cyclic dominance in ecology and microbiology. In a static environment, these models are characterized by fixation probabilities obeying two different "laws" in large and small well-mixed…
A five-species predator-prey model is studied on a square lattice where each species has two prey and two predators on the analogy to the Rock-Paper-Scissors-Lizard-Spock game. The evolution of the spatial distribution of species is…
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…
Biodiversity is essential to the viability of ecological systems. Species diversity in ecosystems is promoted by cyclic, non-hierarchical interactions among competing populations. Such non-transitive relations lead to an evolution with…
A two-type two-sex branching process is introduced with the aim of describing the interaction of predator and prey populations with sexual reproduction and promiscuous mating. In each generation and in each species the total number of…
Cyclic (rock-paper-scissors-type) population models serve to mimic complex species interactions. Focusing on a paradigmatic three-species model with mutations in one dimension, we observe an interplay between equilibrium and non-equilibrium…
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…
We aim to clarify the relationship between interacting three-species models and the two-species Lotka-Volterra (LV) model. We utilize mean-field theory and Monte Carlo simulations on two-dimensional square lattices to explore the temporal…
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…
We investigate a class of continuum models for the motion of a two-dimensional biological group under the influence of nonlocal social interactions. The dynamics may be uniquely decomposed into incompressible motion and potential motion.…
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…
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…
Spatial many-species predator-prey systems have been shown to yield very rich space-time patterns. This observation begs the question whether there exist universal mechanisms for generating this type of emerging complex patterns in…
Rock-paper-scissors (RPS) game is a nice model to study the biodiversity in ecosystem. However, the previous studies only consider the nearest- neighbor- interaction among the species. In this paper, taking the long range migration into…
We study the generalised rock-paper-scissors game with five species whose organisms face local epidemic outbreaks. As an evolutionary behavioural survival strategy, organisms of one out of the species move in the direction with more enemies…
When three species compete cyclically in a well-mixed, stochastic system of $N$ individuals, extinction is known to typically occur at times scaling as the system size $N$. This happens, for example, in rock-paper-scissors games or…
Species diversity in ecosystems is often accompanied by the self-organisation of the population into fascinating spatio-temporal patterns. Here, we consider a two-dimensional three-species population model and study the spiralling patterns…
The spatial rock-paper-scissors ecosystem, where three species interact cyclically, is a model example of how spatial structure can maintain biodiversity. We here consider such a system for a broad range of interaction rates. When one…
Understanding the mechanisms that govern species coexistence and biodiversity represents a fundamental challenge in ecology. This study extends the classic rock-paper-scissors model by introducing a context-dependent higher-order…
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…