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Paladins as predators: Invasive waves in a spatial evolutionary adversarial game

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  • Invasive waves are numerically found in a variant of a reaction-diffusion system used to extend an evolutionary adversarial game into space wherein the influence of various strategies is allowed to diffuse. The diffusion of various strategies corresponds to peer-pressure. The invasive waves are driven by a nonlinear instability that enables an otherwise unstable state to travel through an initially uncooperative state leaving a cooperative state behind. The wave speed's dependence on the various diffusion parameters is examined in one- and two-dimensions through numerically solving the reaction-diffusion equations. Various other phenomena, such as pinning near a diffusive inhomogeneity, are also explored.
    Mathematics Subject Classification: Primary: 35K57, 92D25; Secondary: 91A22.


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