Nonlinear feature of the abrupt transitions between multiple equilibria states of an ecosystem model

Based on a five-variable theoretical ecosystem model, the stability of equilibrium state and the nonlinear feature of the transition between a grassland state and a desert state are investigated. The approach of the conditional nonlinear optimal perturbations (CNOPs), which are the nonlinear generalization of the linear singular vectors (LSVs), is adopted. The numerical results indicate that the linearly stable grassland and desert states are nonlinearly unstable to large enough initial perturbations on the condition that the moisture index μ satisfies 0.3126 < μ < 0.3504. The perturbations represent some kind of anthropogenic influence and natural factors. The results obtained by CNOPs, LSVs and Lyapunov vectors (LVs) are compared to analyze the nonlinear feature of the transition between the grassland state and the desert state. Besides this, it is shown that the five-variable model is superior to the three-variable model in providing more visible signals when the transitions occur.