"Coarse" stability and bifurcation analysis using stochastic simulators: Kinetic Monte Carlo examples

A discussion was presented on the implementation of a computer-assisted approach that, under appropriate conditions, allowed the bifurcation analysis of the 'coarse' dynamic behavior of microscopic simulators without requiring the explicit derivation of closed macroscopic equations. The approach was illustrated through the computation of both stable and unstable coarsely invarient states for kinetic Monte Carlo models of three simple surface reaction schemes. The linearized stability of these coarsely invariant states was quantified alongwith performing of pseudoarclength continuation, detection of coarse limit point and coarse Hopf bifurcations and construction of two-parameter bifurcation diagrams.