He is the author of the Barkley Model of excitable media[5][6] and discoverer of the role of Euclidean symmetry in spiral-wave dynamics.
[8] He has applied this approach in several areas of fluid dynamics, in particular to stability analysis of the cylinder wake[9] and of the backward-facing step.
"[17] In 2005 he was awarded the J. D. Crawford Prize for outstanding research in nonlinear science, "for his development of high quality, robust and efficient numerical algorithms for pattern formation phenomena in spatially extended dynamical systems".
[18][19] In 2008 he was elected Fellow of the American Physical Society "for combining computation and dynamical systems analyses to obtain remarkable insights into hydrodynamic instabilities and patterns in diverse systems, including flow past a cylinder, channel flow, laminar-turbulent bands, and thermal convection.
[21] In 2016 he was elected Fellow of the Society for Industrial and Applied Mathematics "for innovative combinations of analysis and computation to obtain fundamental insights into complex dynamics of spatially extended systems.