This study explores transient spatiotemporal chaos on regular and complex networks with diffusive coupling between the excitable dynamical elements at network nodes. The combined use of theoretical concepts from statistical physics, dynamical systems, statistical mathematics, and numerical modeling is required to improve the understanding of transient spatiotemporal chaos in these systems with a similar steady state dynamics. The purpose of this project is to provide 1) insight from a linear stability analysis into the discriminating properties of the master stability function for transient and asymptotic spatiotemporal chaos for reaction-diffusion networks; 2) a quantification of statistical collapse properties in the Gray-Scott reaction-diffusion network; 3) an identification of local dynamical and topological consequences of nonlocal coupling for the asymptotic stability of the global network dynamics; 4) an identification of common mathematical collapse properties and their robustness against nonlocal coupling. 5) benchmark calculations that will provide a first step towards a generalization/classification of transient spatiotemporal chaos in reaction-diffusion networks as a basis for a more general mathematical theory on transient spatiotemporal chaos. Broader impacts include new insights regarding collapse processes in natural systems, like species extinction in ecology or molecular biology. The educational efforts will focus on research training of diverse undergraduate and graduate students in an interdisciplinary environment where students gain insight into possibilities for diverse careers. Students from other universities will be engaged through the University's REU (Research Experiences for Undergraduates) program. The research results will be presented to the non-scientific public on a Web site, and through the PI's outreach activities in Alaska.
