Nonlinear instability and sensitivity of a theoretical grassland ecosystem to finite-amplitude perturbations

Within a theoretical model context, the sensitivity and instability of the grassland ecosystem to finite-amplitude perturbations are studied. A new approach of conditional nonlinear optimal perturbations (CNOPs) is adopted to investigate this nonlinear problem. It is shown that the linearly stable grassland (desert) states can be nonlinearly unstable with finite-amplitude initial perturbations, which represent the human activities and natural factors on the ecosystem. When the moisture index is between the two bifurcation points, a large enough finite amplitude perturbation can induce a transition from the grassland (desert) state to the desert (grassland) state. The thresholds of such transition along the bifurcation diagram of the moisture index are also given by the CNOPs approach. The results also support the viewpoint of Zeng et al., whose emphasis is on the shading effect of wilted grass on the grassland ecosystem. Comparisons between the results obtained by approach of CNOPs and linear singular vectors are made, which demonstrates that CNOPs is a useful tool to explore the nonlinear features of the ecosystem.