Cyclical interactions with alliance-specific heterogeneous invasion rates.
We study a six-species Lotka-Volterra-type system on different two-dimensional lattices when each species has two superior and two inferior partners. The invasion rates from predator sites to a randomly chosen neighboring prey site depend on the predator-prey pair, whereby cyclic symmetries within the two three-species defensive alliances are conserved. Monte Carlo simulations reveal an unexpected nonmonotonous dependence of alliance survival on the difference of alliance-specific invasion rates. This behavior is qualitatively reproduced by a four-point mean-field approximation. The study addresses fundamental problems of stability for the competition of two defensive alliances and thus has important implications in natural and social sciences.
Department of Physics, Faculty of Education, University of Maribor, Koroska cesta 160, Maribor, Slovenia.
Matjaz
M
Perc
Attila
A
Szolnoki
György
G
Szabó