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Advances in Meteorology
Volume 2015, Article ID 215367, 10 pages
Research Article

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

Bo Wang1,2,3 and Qianqian Qi3

1Institute of Applied Mathematics, Henan University, Kaifeng, Henan 475004, China
2LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
3School of Mathematics and Statistics, Henan University, Kaifeng, Henan 475004, China

Received 19 June 2014; Accepted 2 September 2014

Academic Editor: Hann-Ming H. Juang

Copyright © 2015 Bo Wang and Qianqian Qi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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).