Snowdrift game induces pattern formation in systems of self-propelled particles

Abstract

Evolutionary games between species are known to lead to intriguing spatio-temporal patterns in systems of diffusing agent. However, the role of inter-species interactions is hardly studied when agents are (self-)propelled, as is the case in many biological systems. Here, we combine aspects from active-matter and evolutionary game theory and study a system of two species whose individuals are (self-)propelled and interact through a snowdrift game. We derive hydrodynamic equations for the density and velocity fields of both species from which we identify parameter regimes in which one or both species form macroscopic orientational order as well as regimes of propagating wave patterns. Interestingly, we find simultaneous wave patterns in both species that result from the interplay between alignment and snowdrift interactions - a feedback mechanism that we call game-induced pattern formation. We test these results in agent-based simulations and confirm the different regimes of order and spatio-temporal patterns as well as game-induced pattern formation.

arXiv comment28 pages, 15 figures

References in corpus (26)

• Novel type of phase transition in a system of self-driven particles
• Collective motion
• The Mechanics and Statistics of Active Matter
• Motility-Induced Phase Separation
• Onset of collective and cohesive motion
• Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
• Collective motion of self-propelled particles interacting without cohesion
• Phase transitions and volunteering in spatial public goods games
• The outbreak of cooperation among success-driven individuals under noisy conditions
• Boltzmann and hydrodynamic description for self-propelled particles
• Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
• Self-Propelled Rods: Insights and Perspectives for Active Matter
• Genetic Demixing and Evolutionary Forces in the One-Dimensional Stepping Stone Model
• Phase Transitions and Spatio-Temporal Fluctuations in Stochastic Lattice Lotka-Volterra Models
• Stochastic population dynamics in spatially extended predator-prey systems
• Simple and faithful nonlinear field equations for aligning self-propelled rods
• Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models
• Emergent spatial structures in flocking models: a dynamical system insight
• Chemical warfare and survival strategies in bacterial range expansions
• Active Curved Polymers form Vortex Patterns on Membranes
• Continuous theory of active matter systems with metric-free interactions
• Pattern-induced local symmetry breaking in active matter systems
• Numerical treatment of the Boltzmann equation for self-propelled particle systems
• Mobility, fitness collection, and the breakdown of cooperation
• On the role of multiple scales in metapopulations of public good producers
• Delays in fitness adjustment can lead to coexistence of hierarchically interacting species