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.