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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 619721, 11 pages
Research Article

Bifurcations and Periodic Solutions for an Algae-Fish Semicontinuous System

1School of Life and Environmental Science, Wenzhou University, Wenzhou, Zhejiang 325027, China
2Zhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang 325035, China
3Institute of Mathematics, Academia Sinica, Beijing 100080, China

Received 2 September 2013; Accepted 26 September 2013

Academic Editor: Carlo Bianca

Copyright © 2013 Chuanjun Dai 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.


We propose an algae-fish semicontinuous system for the Zeya Reservoir to study the control of algae, including biological and chemical controls. The bifurcation and periodic solutions of the system were studied using a Poincaré map and a geometric method. The existence of order-1 periodic solution of the system is discussed. Based on previous analysis, we investigated the change in the location of the order-1 periodic solution with variable parameters and we described the transcritical bifurcation of the system. Finally, we provided a series of numerical results to illustrate the feasibility of the theoretical results. These results may help to facilitate a better understanding of algal control in the Zeya Reservoir.