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

Scott G. McCalla

doi:10.3934/dcdsb.2014.19.1437

Article Contents

2014, Volume 19, Issue 5: 1437-1457. Doi: 10.3934/dcdsb.2014.19.1437

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

Scott G. McCalla^1,

1.
Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095

Received: March 2012

Revised: August 2012

Published: July 2014

Abstract / Introduction Related Papers Cited by

Abstract

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.

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Mathematics Subject Classification: Primary: 35K57, 92D25; Secondary: 91A22.

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