… These perform various types of stability analyses: linear stability analysis via the … analysis
of a limit cycle, and nonlinear stability analysis for determining the character of a bifurcation. All …

… The Model The example we chose to demonstrate the coarse bifurcation analysis concept
is one where the mean-field PDE is available, in order to assess the performance of RPM …

… We discuss how matrix-free/timestepper algorithms can efficiently be used with dynamic
non… stability/bifurcation analysis. The timestepper approach to bifurcation analysis of large-scale …

… 83 2857–60 [42] Theodoropoulos C, Qian YH and Kevrekidis IG 2000 ‘Coarse’ stability
and bifurcation analysis using timesteppers: a reaction–diffusion example Proc. Natl. Acad. …

We show how the Equation Free approach for multi-scale computations can be exploited to
extract, in a computational rigorous and systematic way the emergent dynamical attributes, …

… We then look at the mathematics of time-steppers, … bifurcations of the original dynamical
system. In addition, we explain why time-steppers are not well suited for bifurcation analysis. …

… Bifurcation analysis … Bifurcation diagrams represent families of equilibria and periodic orbits
as curves or surfaces in appropriate coordinate systems. Special points, such as bifurcations, …

… For the systematic and effective analysis of the simulation dynamics, one has to resort to
bifurcation analysis. Numerical bifurcation theory provides an arsenal of algorithms and …

… Similar to [25] we will adopt a ‘bifurcation analysis for timesteppers’ approach that allows
these analyses to be undertaken after a reasonably straightforward modification of a time…

… Similar to [1], we will adopt a ‘bifurcation analysis for timesteppers’ approach that allows
these analyses to be undertaken after a reasonably straightforward modification of a time-…