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arXiv · 0901.0955

Four-state rock-paper-scissors games on constrained Newman-Watts networks

Guo-Yong Zhang·Yong Chen·Wei-Kai Qi·Shao-Meng Qin
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Abstract

We study the cyclic dominance of three species in two-dimensional constrained Newman-Watts networks with a four-state variant of the rock-paper-scissors game. By limiting the maximal connection distance $R_{max}$ in Newman-Watts networks with the long-rang connection probability $p$, we depict more realistically the stochastic interactions among species within ecosystems. When we fix mobility and vary the value of $p$ or $R_{max}$, the Monte Carlo simulations show that the spiral waves grow in size, and the system becomes unstable and biodiversity is lost with increasing $p$ or $R_{max}$. These results are similar to recent results of Reichenbach \textit{et al.} [Nature (London) \textbf{448}, 1046 (2007)], in which they increase the mobility only without including long-range interactions. We compared extinctions with or without long-range connections and computed spatial correlation functions and correlation length. We conclude that long-range connections could improve the mobility of species, drastically changing their crossover to extinction and making the system more unstable.

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Guo-Yong Zhang, Yong Chen, Wei-Kai Qi, Shao-Meng Qin. 2009-07-03. Four-state rock-paper-scissors games on constrained Newman-Watts networks. https://doi.org/10.1103/physreve.79.062901

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