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Mathematical Problems in Engineering
Volume 2013, Article ID 731042, 9 pages
Research Article

Nonsmooth Dynamic Behaviors Inherited from an Ecohydrological Model: Mutation, Bifurcation, and Chaos

1School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081, China
2Department of Hydraulic Engineering, State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China
3Key Laboratory of Northwest Water Resources and Environmental Ecology of MOE, Xi'an University of Technology, Xi'an 710048, China

Received 17 December 2012; Accepted 28 January 2013

Academic Editor: Yongping Li

Copyright © 2013 Mu Lin 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 existence of nontrivial dynamic behaviors in a hydrological system is intensively discussed in the literature. However, most of the work has been done from the nonlinear data analysis perspective, with only a few exceptions, due to the mathematical difficulties for theoretical analysis. In this study, a simple but comprehensive enough ecohydrological model with the pulsed atmospheric forcing was developed from the process analysis perspective. The model was then utilized to analyze the non-trivial dynamic behaviors in a coupled ecohydrological system qualitatively and numerically. Our results confirm the existence of multiple stationary states discussed by many researchers. Furthermore, parameter bifurcation was studied and the phenomenon of mutation is found to be rather common. Also, the chaotic characteristic of the system state is obtained under some specific parameters. Parts of these behaviors were seldom reported through the deterministic dynamic analysis done previously.