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

@article{Avelino2012JunctionsAS, title={Junctions and spiral patterns in generalized rock-paper-scissors models.}, author={Pedro 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={2012}, volume={86 3 Pt 2}, pages={ 036112 } }

We investigate the population dynamics in generalized rock-paper-scissors models with an arbitrary number of species N. We show 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. While the former case gives rise to an interface network with Y-type junctions obeying the scaling law L∝t1/2, where L is the…

## 58 Citations

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- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

It is argued that the results are expected to be quite generic in the context of spatial stochastic May-Leonard models, and it is shown that the macroscopic evolution of the interface network is not very sensitive to the internal structure of the interfaces.

### The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games

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It is shown that the spiral waves predicted by the system's deterministic partial equations are found in lattice simulations only within a finite range of the mobility rate, and that in the absence of mutations and dominance-replacement, the resulting spiraling patterns are subject to convective instability and far-field breakup at low mobility rate.

### Uneven rock-paper-scissors models: Patterns and coexistence

- Environmental ScienceEPL (Europhysics Letters)
- 2019

The coexistence probability is investigated and it is shown that the surviving species depends on the level of unevenness of the model and the mobility of individuals, and the asymmetry in the selection probabilities leads to different spatial autocorrelation function and average relative species abundances.

### Mobility unevenness in rock-paper-scissors models

- Environmental Science
- 2022

We investigate a tritrophic system whose cyclic dominance is modelled by the rock-paper-scissors game. We consider that organisms of one or two species are a ﬀ ected by movement limitations, which…

### Performance of weak species in the simplest generalization of the rock-paper-scissors model to four species.

- Environmental SciencePhysical review. E
- 2020

It is shown, using lattice based spatial stochastic simulations with random initial conditions, that if only one of the four species has its probability reduced, then the most abundant species is the prey of the "weakest" (assuming that the simulations are large enough for coexistence to prevail).

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- MathematicsPhysical review. E
- 2019

It is found that the relatively large oscillations at the initial stages of simulations with random initial conditions may result in a significant dependence of the probability of species survival on the lattice size.

### Spirals and coarsening patterns in the competition of many species: a complex Ginzburg–Landau approach

- Mathematics
- 2014

For large classes of systems the space of coexistence fixed points at which biodiversity is maximal is determined, starting from the deterministic mean-field rate equations, and complex Ginzburg-Landau equations are derived that allow for space-time pattern realized in two space dimensions.

### Expanding spatial domains and transient scaling regimes in populations with local cyclic competition.

- MathematicsPhysical review. E
- 2019

It is shown that a transient scaling regime, with a slower average growth rate of the characteristic length scale L of the spatial domains with time t, takes place before the transition to a standard L∝t^{1/2} scaling law, resulting in an extended period of coexistence.

### Invasion-controlled pattern formation in a generalized multispecies predator-prey system.

- Environmental SciencePhysical review. E
- 2019

This study generalizes a four-state predator-prey-type model and reveals an exceptional richness of pattern formations where five quantitatively different phases are observed by varying solely the strength of the mentioned inner invasion.

### Interface networks in models of competing species

- MathematicsInt. J. Model. Simul. Sci. Comput.
- 2018

All the results provided by the soliton topological model are in agreement with the stochastic simulations and may be used as a tool for understanding the complex biodiversity in nature.

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