Least squares shadowing sensitivity analysis of a modified Kuramoto–Sivashinsky equation

•Modifying the Kuramoto–Sivashinsky equation and changing its boundary conditions make it an ergodic dynamical system.•The modified Kuramoto–Sivashinsky equation exhibits distinct dynamics for three different ranges of system parameters.•Least squares shadowing sensitivity analysis computes accurate gradients for a wide range of system parameters.

Computational methods for sensitivity analysis are invaluable tools for scientists and engineers investigating a wide range of physical phenomena. However, many of these methods fail when applied to chaotic systems, such as the Kuramoto–Sivashinsky (K–S) equation, which models a number of different chaotic systems found in nature. The following paper discusses the application of a new sensitivity analysis method developed by the authors to a modified K–S equation. We find that least squares shadowing sensitivity analysis computes accurate gradients for solutions corresponding to a wide range of system parameters.