Rock-paper-scissors played within competing domains in predator-prey games
Rock-paper-scissors played within competing domains in predator-prey games
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DOI：
10.1088/1742-5468/2016/11/113402
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发表时间：
2016-08
期刊：
影响因子：
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通讯作者：
Darka Labavi'c;H. Meyer-Ortmanns
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文献类型：
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作者：
Darka Labavi'c;H. Meyer-Ortmanns
我们考虑具有N个种群且r < N的捕食者和被捕食者的（N，r）捕食与被捕食博弈，其行为是循环的.进一步的基本反应包括在一维或二维规则网格上的复制、衰变和扩散，而没有对每个位点的占用数量的硬性约束，因此在“玻色子”实现中。对于N和r的特殊组合以及适当的参数选择，我们观察到游戏中的游戏，即不同的共存游戏，这取决于空间分辨率。作为一个具体而简单的例子，我们分析了（6，3）博弈。一旦参与者从随机的初始分布中分离出来，域就出现了，它有效地在域直径的粗略尺度上玩（2，1）游戏，而域内部的代理人则玩（3，1）（剪刀石头布），导致物种相互追逐的螺旋形形成。（2，1）-博弈最终会有一个赢家，所以域的共存是短暂的，而剩余域内的代理人共存，直到人口波动导致所有物种灭绝，只有一个物种最终灭绝。这意味着，我们观察到一个动态生成的多个空间和时间尺度与新兴的重新组织的球员隔离后，从一个简单的一套规则的最小规模（即网格）和改变规则，从粗糙的角度。这些观测结果是基于吉莱斯皮的模拟。讨论了由货车坎彭展开式导出的确定性极限。在此极限下，我们进行线性稳定性分析，并对所得方程进行数值积分。线性稳定性分析预测了形成域的数量，它们的组成在物种方面;它解释了域之间的界面的不稳定性，这驱动它们的灭绝;螺旋图案被确定为运动沿着异宿周期。数值解再现了吉莱斯皮模拟中观察到的模式，甚至包括灭绝事件，因此这里的平均场分析是非常有说服力的，这是由于规则的具体实施。
We consider (N, r) games of prey and predation with N species and r < N prey and predators, acting in a cyclic way. Further basic reactions include reproduction, decay and diffusion over a one- or two-dimensional regular grid, without a hard constraint on the occupation number per site, so in a ‘bosonic’ implementation. For special combinations of N and r and appropriate parameter choices we observe games within games, that is different coexisting games, depending on the spatial resolution. As a concrete and simplest example we analyze the (6,3) game. Once the players segregate from a random initial distribution, domains emerge, which effectively play a (2,1)-game on the coarse scale of domain diameters, while agents inside the domains play (3,1) (rock-paper-scissors), leading to spiral formation with species chasing each other. The (2,1)-game has a winner in the end, so that the coexistence of domains is transient, while agents inside the remaining domain coexist, until demographic fluctuations lead to extinction of all but one species in the very end. This means that we observe a dynamical generation of multiple space and time scales with emerging re-organization of players upon segregation, starting from a simple set of rules on the smallest scale (that of the grid) and changed rules from the coarser perspective. These observations are based on Gillespie simulations. We discuss the deterministic limit derived from a van Kampen expansion. In this limit we perform a linear stability analysis and numerically integrate the resulting equations. The linear stability analysis predicts the number of forming domains, their composition in terms of species; it explains the instability of interfaces between domains, which drives their extinction; spiral patterns are identified as motion along heteroclinic cycles. The numerical solutions reproduce the observed patterns of the Gillespie simulations including even extinction events, so that the mean-field analysis here is very conclusive, which is due to the specific implementation of rules.