Spirals and heteroclinic cycles in a spatially extended Rock-Paper-Scissors model of cyclic dominance
نویسندگان
چکیده
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 profiles reminiscent of heteroclinic cycles. We compute numerically a nonlinear dispersion relation between the wavelength and wavespeed of the traveling waves, and, together with insight from heteroclinic bifurcation theory and further numerical results from 2D simulations, we are able to make predictions about the overall structure and stability of spiral waves in 2D cyclic dominance models.
منابع مشابه
Three-state Potts model in combination with the rock-scissors-paper game.
We study a three-state Potts model extended by allowing cyclic dominance between the states as exemplified in the rock-scissors-paper game. Monte Carlo simulations are performed on a square lattice while varying the temperature and the strength of cyclic dominance. It is shown that the critical phase transition from the disordered state to the ordered one is destroyed by the cyclic dominance, w...
متن کاملThree- and four-state rock-paper-scissors games with diffusion.
Cyclic dominance of three species is a commonly occurring interaction dynamics, often denoted the rock-paper-scissors (RPS) game. Such a type of interactions is known to promote species coexistence. Here, we generalize recent results of Reichenbach [Nature (London) 448, 1046 (2007)] of a four-state variant of the RPS game. We show that spiral formation takes place only without a conservation la...
متن کاملStochastic population dynamics in spatially extended predator-prey systems
Spatially extended population dynamics models that incorporate demographic noise serve as case studies for the crucial role of fluctuations and correlations in biological systems. Numerical and analytic tools from non-equilibrium statistical physics capture the stochastic kinetics of these complex interacting manyparticle systems beyond rate equation approximations. Including spatial structure ...
متن کاملSelf-organization of mobile populations in cyclic competition.
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 'rock-paper-scissors' game. Both experimentally and theoretically, such non-transitive interactions have been found to induce self-organization of static individuals i...
متن کاملVortices determine the dynamics of biodiversity in cyclical interactions with protection spillovers
If rock beats scissors and scissors beat paper, onemight assume that rock beats paper too. But this is not the case for intransitive relationships thatmake up the famous rock-paper-scissors game. However, the sole presence of papermight prevent rock frombeating scissors, simply because paper beats rock. This is the blueprint for the rock-paper-scissors gamewith protection spillovers, which has ...
متن کامل