Investigate sensitivity computation for the Lotka-Volterra equations

[Schlevidon]

Summary

During the IFDIFF workshop participants were puzzled by the sensitivity plots produced by the plotSensitivities function (only available in the workshop branch) for the Lotka-Volterra equations. The magnitude of the sensitivities continually increases over the time horizon, contrary to the expected behavior of the magnitude staying bounded due to the fact that the magnitude of the trajectories is bounded.
Investigate whether this behavior is correct or if there is an issue with the sensitivity computations. This is not a critical task!

Proposed approaches

• Conduct theoretical research on the sensitivities of the Lotka-Volterra equations. Ideally find a trustworthy source which shows the correct sensitivities.
• Alternatively, try to determine experimentally if the increasing magnitude is a numerical artifact caused by the solver.
  • Check if the integrator tolerance has an influence on the solution.
  • Check if the step size of the finite differences (FD) method has an influence on the solution.