Four-state rock-paper-scissors games in 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 Rmax in Newman-Watts networks with the long-range 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 Rmax, 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 Rmax. These results are similar to recent results of Reichenbach et al. [Nature (London) 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.
Zhang
Guo-Yong
GY
Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China.
Chen
Yong
Y
Qi
Wei-Kai
WK
Qing
Shao-Meng
SM
D000465:Algorithms; D005075:Biological Evolution; D003198:Computer Simulation; D017753:Ecosystem; D020387:Food Chain; D005716:Game Theory; D008954:Models, Biological; D011157:Population Dynamics