The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games

Abstract

We consider a two-dimensional model of three species in rock-paper-scissors competition and study the self-organisation of the population into fascinating spiraling patterns. Within our individual-based metapopulation formulation, the population composition changes due to cyclic dominance (dominance-removal and dominance-replacement), mutations, and pair-exchange of neighboring individuals. Here, we study the influence of mobility on the emerging patterns and investigate when the pair-exchange rate is responsible for spiral waves to become elusive in stochastic lattice simulations. In particular, we show that the spiral waves predicted by the system's deterministic partial equations are found in lattice simulations only within a finite range of the mobility rate. We also report that in the absence of mutations and dominance-replacement, the resulting spiraling patterns are subject to convective instability and far-field breakup at low mobility rate. Possible applications of these resolution and far-field breakup phenomena are discussed.

20 pages, 5 figures; published in Games

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Cited by in corpus (15)

• Stochastic population dynamics in spatially extended predator-prey systems
• Strategy dependent learning activity in cyclic dominant systems
• Hamming distance and mobility behavior in generalized rock-paper-scissors models
• Effect of mobility in the rock-paper-scissor dynamics with high mortality
• Invasion controlled pattern formation in a generalized multi-species predator-prey system
• Competition of alliances in a cyclically dominant eight-species population
• Basin entropy behavior in a cyclic model of the rock-paper-scissors type
• Emerging solutions from the battle of defensive alliances
• Environment driven oscillation in an off-lattice May--Leonard model
• Equal partners do better in defensive alliances
• When faster rotation is harmful: the competition of alliances with inner blocking mechanism
• Effects of a pestilent species on the stability of cyclically dominant species
• Oppressed species can form a winning pair in a multi-species ecosystem
• Competition among alliances of different sizes
• Non-Markovian Rock-Paper-Scissors games