Interfaces with internal structures in generalized rock-paper-scissors models.

@article{Avelino2013InterfacesWI,
  title={Interfaces with internal structures in generalized rock-paper-scissors models.},
  author={Pedro P Avelino and Dionisio Bazeia and L. Losano and J. Menezes and B. F. de Oliveira},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2013},
  volume={89 4},
  pages={
          042710
        }
}
In this work we investigate the development of stable dynamical structures along interfaces separating domains belonging to enemy partnerships in the context of cyclic predator-prey models with an even number of species N≥8. We use both stochastic and field theory simulations in one and two spatial dimensions, as well as analytical arguments, to describe the association at the interfaces of mutually neutral individuals belonging to enemy partnerships and to probe their role in the development… 
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References

SHOWING 1-10 OF 39 REFERENCES

Junctions and spiral patterns in generalized rock-paper-scissors models.

It is shown that spiral patterns with N arms may develop both for odd and even N, in particular in models where a bidirectional predation interaction of equal strength between all species is modified to include one N-cyclic predator-prey rule.

Extinction in neutrally stable stochastic Lotka-Volterra models.

A new method based on stochastic averaging is introduced which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics.

Segregation process and phase transition in cyclic predator-prey models with an even number of species.

A spatial cyclic predator-prey model with an even number of species that allows the formation of two defensive alliances consisting of the even and odd label species is studied.

Cyclic competition of four species: domains and interfaces

In two space dimensions, when also exchanges between mutually neutral particles are possible, both domain growth and interface fluctuations display universal regimes that are independent of the predation and exchange rates.

Competing associations in six-species predator–prey models

Under some conditions the survival of all the species can be maintained by the cyclic dominance occurring between these associations, and under some conditions larger and larger invasion processes precede the prevalence of one of the stable associations.

Segregation in a One-Dimensional Model of Interacting Species.

This work investigates segregation and spatial organization in a one-dimensional system of N competing species forming a cyclic food chain and presents scaling arguments as well as numerical simulations for the leading asymptotic behavior of the density of interfaces separating neighboring domains.

Defensive alliances in spatial models of cyclical population interactions.

  • G. SzabóT. Czárán
  • Biology
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2001
Cyclical interaction models of six mutating species are studied on a square lattice, in which each species is supposed to have two dominant, two subordinated, and a neutral interacting partner, resulting in an ordering phenomenon analogous to that of magnetic Ising systems.

Intransitivity and coexistence in four species cyclic games.

Mobility promotes and jeopardizes biodiversity in rock–paper–scissors games

It is established that this phenomenon is robust; it does not depend on the details of cyclic competition or spatial environment, and are relevant for the formation and propagation of patterns in microbial populations or excitable media.

Noise and correlations in a spatial population model with cyclic competition.

A paradigmatic spatial model where three species exhibit cyclic dominance is considered, using an individual-based description, as well as stochastic partial differential and deterministic reaction-diffusion equations, and it is shown how fascinating patterns of entangled spirals emerge.