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In the shallow lake ecosystems, the recovery of the aquatic macrophytes and the increase in the water transparency have been the main contents of the ecological restoration. Using the shallow lake ecological degradation and restoration model, CNOP method is adopted to discuss the instability and sensitivity of the ecosystem to the finite-amplitude perturbations related to the initial condition and the parameter condition. Results show that the linearly stable clear (turbid) water states can be nonlinearly unstable with the finite-amplitude perturbations, which represent the nature factors and the human activities such as the excessive harvest of the macrophytes and the sediment resuspension caused by artificially dynamic actions on the ecosystems. The results also support the viewpoint of Scheffer et al., whose emphasis is that the facilitation interactions between the submerged macrophytes and the water transparency are the main trigger for an occasional shift from a turbid to a clear state. Also, by the comparison with CNOP-I, CNOP-P, CNOP, and (CNOP-I, CNOP-P), results demonstrate that CNOP, which is not a simple combination of CNOP-I and CNOP-P, could induce the shallow lake ecosystem larger departure from the same ground state rather than CNOP-I, CNOP-P, and (CNOP-I, CNOP-P)

Application of the Conditional Nonlinear Optimal Perturbations Method in the Shallow Lake Ecological Degradation and Restoration