The Role of Bifurcations in Parameter Estimation: A UQ Analysis of the Non-spatial Klausmeier Model

Abstract

We employ uncertainty quantification methods to investigate how parameter identifiability changes in the vicinity of a bifurcation point. We perform numerical experiments on the non-spatial Klausmeier vegetation model with random coefficients, which describes biomass-water interactions and exhibits a fold bifurcation. We partition the domain around the bifurcation into regions with distinct convergence behaviors. In each region, we follow a UQ workflow that includes sensitivity analysis, Bayesian inference, and Fisher information evaluation to assess parameter identifiability. The results show that proximity to the bifurcation point is decisive for parameter estimation. Reliable joint inference of both model parameters is not possible when the system exhibits bistability. Furthermore, we can reconstruct the model's bifurcation pattern by Fisher information heatmaps, presenting a practical tool for bifurcation detection. Lastly, we highlight the importance of transient data for successful parameter estimation.