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Four-state rock-paper-scissors games on constrained Newman-Watts networks
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 in Newman-Watts
networks with the long-rang connection probability , we depict more
realistically the stochastic interactions among species within ecosystems. When
we fix mobility and vary the value of or , the Monte Carlo
simulations show that the spiral waves grow in size, and the system becomes
unstable and biodiversity is lost with increasing or . 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.Comment: 6 pages, 7 figure
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