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Advances in Meteorology
Volume 2012, Article ID 562081, 7 pages
Research Article

The Sensitivity Analysis of a Lake Ecosystem with the Conditional Nonlinear Optimal Perturbation Method

1Institute of Applied Mathematics, Henan University, Henan Kaifeng 475004, China
2College of Mathematics and Information Science, Henan University, Henan Kaifeng 475004, China
3Key Laboratory of Ocean Circulation and Wave, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China

Received 4 April 2012; Revised 6 June 2012; Accepted 23 June 2012

Academic Editor: Wansuo Duan

Copyright © 2012 Bo Wang et al. 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.


The instability and sensitivity of a lake ecosystem to the finite-amplitude perturbations related to the initial condition and the parameter correspondingly are studied. The CNOP-I and CNOP-P methods are adopted to investigate this nonlinear system. The numerical results with CNOP-I method show that the lake ecosystem can be nonlinearly unstable with finite-amplitude initial perturbations when the nutrient loading rate is between the two bifurcation points. A large enough finite amplitude initial perturbation, that is, CNOP-I, can induce a transition from an oligotrophic (eutrophic) state to an eutrophic (oligotrophic) state. With CNOP-P method, it is shown that the lake ecosystem can be transformed from an oligotrophic (eutrophic) state to an eutrophic (oligotrophic) state with a large enough finite amplitude parameter perturbation, that is, CNOP-P, no matter how large the nutrient loading rate is.