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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 171793, 10 pages
Research Article

Modeling and Dynamical Analysis of the Water Resources Supply-Demand System: A Case Study in Haihe River Basin

State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing 100875, China

Received 15 March 2014; Accepted 8 May 2014; Published 26 May 2014

Academic Editor: Song Cen

Copyright © 2014 Chongli Di and Xiaohua Yang. 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 relationship between water resources supply and demand is very complex and exhibits nonlinear characteristics, which leads to fewer models that can adequately manage the dynamic evolution process of the water resources supply-demand system. In this paper, we propose a new four-dimensional dynamical model to simulate the internal dynamic evolution process and predict future trends of water supply and demand. At the beginning, a new four-dimensional dynamical model with uncertain parameters is established. Then, the gray code hybrid accelerating genetic algorithm (GHAGA) is adopted to identify the unknown parameters of the system based on the statistic data (1998–2009). Finally, the dynamical analysis of the system is further studied by Lyapunov-exponent, phase portraits, and Lyapunov exponent theory. Numerical simulation results demonstrate that the proposed water resources supply-demand system is in a steady state and is suitable for simulating the dynamical characteristics of a complex water supply and demand system. According to the trends of the water supply and demand of several nonlinear simulation cases, the corresponding measures can be proposed to improve the steady development of the water resources supply-demand system.