Related papers: Characterization of spiraling patterns in spatial …
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 formation of out-of-equilibrium patterns is a characteristic feature of spatially-extended, biodiverse, ecological systems. Intriguing examples are provided by cyclic competition of species, as metaphorically described by the…
We consider a two-dimensional model of three species in rock-paper-scissors competition and study the self-organisation of the population into fascinating spiraling patterns. Within our individual-based metapopulation formulation, the…
We investigate the impact of cyclic competition on pattern formation in the rock-paper-scissors game. By separately considering random and prepared initial conditions, we observe a critical influence of the competition rate $p$ on the…
Noise and spatial degrees of freedom characterize most ecosystems. Some aspects of their influence on the coevolution of populations with cyclic interspecies competition have been demonstrated in recent experiments [e.g. B. Kerr et al.,…
We study a variant of the cyclic Lotka-Volterra model with three-agent interactions. Inspired by a multiplayer variation of the Rock-Paper-Scissors game, the model describes an ideal ecosystem in which cyclic competition among three species…
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…
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…
Organisms may respond to local stimuli that benefit or threaten their fitness. The adaptive movement behaviour may allow individuals to adjust their speed to maximise the chances of being in comfort zones, where death risk is minimal. We…
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…
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…
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…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
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…
We analyze the replicator-mutator equations for the Rock-Paper-Scissors game. Various graph-theoretic patterns of mutation are considered, ranging from a single unidirectional mutation pathway between two of the species, to global…
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…
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…
Spatially extended versions of the cyclic-dominance Rock-Paper-Scissors model have traveling wave (in one dimension) and spiral (in two dimensions) behavior. The far field of the spirals behave like traveling waves, which themselves have…
We study a class of the stochastic May-Leonard models, with three species dominating each other in a cyclic nonhierarchical way, according to the rock-paper-scissors game. We introduce an unevenness in the system, by considering that one of…
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…