SBML Inverse Eigenvalue Analyzer is MathSBML Add-On package that can be used to identify (sparse) parameter sets whose variation from the nominal values can lead to different qualitative dynamics, such as exhibiting bistability or oscillations. The method is based on performing inverse eigenvalue analyses, placing minimal eigenvalues of the ODE system either close to the origin or lie imaginary axis. From the identified parameter solution, subsequent (forward) bifurcation analyses can verify the dynamical behaviors.
The hybrid solution method consists of sequentially carrying out:
- Lift-and-Project iterations;
- Quasi-Newton iterations.
The constrainted nonlinear optimization problem that arises in (1) is solved using the OptimizationToolbox attached to the book 'Practical Optimization Methods with Mathematica Applications' by M. Asghar Bhatti, TELOS 2000. The unconstrained optimization problem is solved using Mathematica built-in function, FindMinimum.