Loop eigenvalue elasticity analysis: three case studies

We explore the application of loop eigenvalue elasticity analysis (LEEA) to three different models in order to assess the potential of the method for generating insights about model behaviour and to uncover issues in developing the method further. The results indicate that the utility of the method depends upon the character of the model and dynamics involved. In models where the transient behaviour is of interest, the method yields insights on a par with the pathway participation method, though better tools to link the method to time paths of particular variables are needed. In quasi-linear models, LEEA shows the most promise, quickly revealing the different behaviour modes and the associated dominant structures. Finally, analysis of a nonlinear chaotic model reveals that the eigenvalues may change rapidly even during phases when the mode of behaviour appears constant, limiting the insights gained from LEEA analysis. The paper concludes with our thoughts on the strengths and weaknesses of the LEEA and suggestions for future work.