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Abstract: We study the cyclic dominance of three species in two-dimensional constrainedNewman-Watts networks with a four-state variant of the rock-paper-scissorsgame. By limiting the maximal connection distance $R {max}$ in Newman-Wattsnetworks with the long-rang connection probability $p$, we depict morerealistically the stochastic interactions among species within ecosystems. Whenwe fix mobility and vary the value of $p$ or $R {max}$, the Monte Carlosimulations show that the spiral waves grow in size, and the system becomesunstable and biodiversity is lost with increasing $p$ or $R {max}$. Theseresults are similar to recent results of Reichenbach \textit{et al.} NatureLondon \textbf{448}, 1046 2007, in which they increase the mobility onlywithout including long-range interactions. We compared extinctions with orwithout long-range connections and computed spatial correlation functions andcorrelation length. We conclude that long-range connections could improve themobility of species, drastically changing their crossover to extinction andmaking the system more unstable.



Autor: Guo-Yong Zhang, Yong Chen, Wei-Kai Qi, Shao-Meng Qin

Fuente: https://arxiv.org/







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