A golden point rule in rock–paper–scissors–lizard–spock game

Kang, Yibin; Pan, Qiuhui; Wang, Xueting; He, Mingfeng

doi:10.1016/j.physa.2012.10.011

Cited by 38 publications

(35 citation statements)

References 36 publications

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“…Much work has been devoted to cyclic cases as for example the three-species cyclic game [21] or the corresponding game with four species where each species is preying on one other species while being at the same time the prey of another species [22][23][24][25][26][27][28][29]. Whereas some earlier papers have considered spatial and stochastic effects in systems with a larger number of species [30][31][32][33][34][35][36][37][38][39][40][41], it is only in the last few years that systematic theoretical studies of more complicated food networks with five or more species 2 have become available [19,[42][43][44][45][46][47][48][49][50][51][52][53][54]. One of the intriguing results of these studies has been the discovery of a rich variety of space-time patterns, including spirals where each wavefront is formed by a single species, fuzzy spirals due to the mixing of different species inside the waves, coarsening domains where every domain is formed by an alliance of mutually neutral species as well as coarsening processes where inside every domain spirals are formed, thus yielding non-trivial dynamics inside the coarsening domains [19,48,51,55].…”

Section: Introductionmentioning

confidence: 99%

Coarsening with nontrivial in-domain dynamics: Correlations and interface fluctuations

Brown

Pleimling

2017

Phys. Rev. E

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Using numerical simulations we investigate the space-time properties of a system in which spirals emerge within coarsening domains, thus giving rise to non-trivial internal dynamics. Initially proposed in the context of population dynamics, the studied six-species model exhibits growing domains composed of three species in a rock-paper-scissors relationship. Through the investigation of different quantities, such as space-time correlations and the derived characteristic length, autocorrelation, density of empty sites, and interface width, we demonstrate that the non-trivial dynamics inside the domains affects the coarsening process as well as the properties of the interfaces separating different domains. Domain growth, aging, and interface fluctuations are shown to be governed by exponents whose values differ from those expected in systems with curvature driven coarsening.

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Section: Introductionmentioning

confidence: 99%

Coarsening with nontrivial in-domain dynamics: Correlations and interface fluctuations

Brown

Pleimling

2017

Phys. Rev. E

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“…Similar studies of more complicated systems composed of multiple species interacting in less trivial ways have been scarce until recently [61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77].…”

Section: Introductionmentioning

confidence: 99%

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

Mowlaei¹,

Roman²,

Pleimling³

2014

J. Phys. A: Math. Theor.

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Abstract. In order to model real ecological systems one has to consider many species that interact in complex ways. However, most of the recent theoretical studies have been restricted to few species systems with rather trivial interactions. The few studies dealing with larger number of species and/or more complex interaction schemes are mostly restricted to numerical explorations. In this paper we determine, starting from the deterministic meanfield rate equations, for large classes of systems the space of coexistence fixed points at which biodiversity is maximal. For systems with a single coexistence fixed point we derive complex Ginzburg-Landau equations that allow to describe space-time pattern realized in two space dimensions. For selected cases we compare the theoretical predictions with the pattern observed in numerical simulations.

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“…Intoy et al focused on the extinction processes in a cyclic four-species system [27]. In our previous work, we studied the evolution properties of a cyclic five-strategy system with two different invasion routes [28], and the group interactions of the system have been discussed [29][30][31]. Knebel et al analyzed the coexistence and survival scenarios of Lotka-Volterra networks with both a cyclic four-species…”

Section: Introductionmentioning

confidence: 99%

A Five Species Cyclically Dominant Evolutionary Game with Fixed Direction: A New Way to Produce Self-Organized Spatial Patterns

Kang

Pan

Wang

et al. 2016

Entropy

Self Cite

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Abstract:Cyclically dominant systems are hot issues in academia, and they play an important role in explaining biodiversity in Nature. In this paper, we construct a five-strategy cyclically dominant system. Each individual in our system changes its strategy along a fixed direction. The dominant strategy can promote a change in the dominated strategy, and the dominated strategy can block a change in the dominant strategy. We use mean-field theory and cellular automaton simulation to discuss the evolving characters of the system. In the cellular automaton simulation, we find the emergence of spiral waves on spatial patterns without a migration rate, which suggests a new way to produce self-organized spatial patterns.

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A golden point rule in rock–paper–scissors–lizard–spock game

Cited by 38 publications

References 36 publications

Coarsening with nontrivial in-domain dynamics: Correlations and interface fluctuations

Coarsening with nontrivial in-domain dynamics: Correlations and interface fluctuations

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

A Five Species Cyclically Dominant Evolutionary Game with Fixed Direction: A New Way to Produce Self-Organized Spatial Patterns

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