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 …

Spatially extended population dynamics models that incorporate demographic noise serve
as case studies for the crucial role of fluctuations and correlations in biological systems …

Complex systems in ecological science can be generally defined by either the number of
different species or the structure among species having many relations, and understanding …

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 …

Evolutionary games of cyclic competitions have been extensively studied to gain insights
into one of the most fundamental phenomena in nature: biodiversity that seems to be …

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 …

The nonequilibrium dynamics of a cycling three-state Potts model is studied on a square
lattice using Monte Carlo simulations and continuum theory. This model is relevant to …

Many types of spatiotemporal patterns have been observed under nonequilibrium
conditions. Cycling through four or more states can provide specific dynamics, such as the …

Cyclic dominance between species may yield spiral waves that are known to provide a
mechanism enabling persistent species coexistence. This observation holds true even in …

We studied the nonequilibrium dynamics of a cycling three-state Potts model using
simulations and theory. This model can be tuned from thermal-equilibrium to far-from …