Dynamically generated hierarchies in games of competition

Abstract

Spatial many-species predator-prey systems have been shown to yield very rich space-time patterns. This observation begs the question whether there exist universal mechanisms for generating this type of emerging complex patterns in non-equilibrium systems. In this work we investigate the possibility of dynamically generated hierarchies in predator-prey systems. We analyze a nine-species model with competing interactions and show that the studied situation results in the spontaneous formation of spirals within spirals. The parameter dependence of these intriguing nested spirals is elucidated. This is achieved through the numerical investigation of various quantities (correlation lengths, densities of empty sites, Fourier analysis of species densities, interface fluctuations) that allows to gain a rather complete understanding of the spatial arrangements and the temporal evolution of the system. A possible generalization of the interaction scheme yielding dynamically generated hierarchies is discussed. As cyclic interactions occur spontaneously in systems with competing strategies, the mechanism discussed in this work should contribute to our understanding of various social and biological systems.

28 pages, 12 figures, accepted for publication in the Physical Review E

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• Environment driven oscillation in an off-lattice May--Leonard model
• Effects of a pestilent species on the stability of cyclically dominant species
• Equal partners do better in defensive alliances
• When faster rotation is harmful: the competition of alliances with inner blocking mechanism
• Competition among alliances of different sizes
• Oppressed species can form a winning pair in a multi-species ecosystem