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

摘要: We implement a computer-assisted approach that, under appropriate conditions, allows the bifurcation analysis of “coarse” dynamic behavior microscopic simulators without requiring explicit derivation closed macroscopic equations for this behavior. The is inspired by so-called time-stepper based numerical theory. illustrate through computation both stable and unstable coarsely invariant states kinetic Monte Carlo models three simple surface reaction schemes. quantify linearized stability these states, perform pseudoarclength continuation, detect coarse limit point Hopf bifurcations, construct two-parameter diagrams.