Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 150359, 12 pages
Research Article

Seasonally Perturbed Prey-Predator Ecological System with the Beddington-DeAngelis Functional Response

1School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, China
2School of Life and Environmental Science, Wenzhou University, Wenzhou, Zhejiang 325027, China

Received 1 October 2011; Accepted 2 November 2011

Academic Editor: Vladimir Gontar

Copyright © 2012 Hengguo Yu and Min Zhao. 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.


On the basis of the theories and methods of ecology and ordinary differential equation, a seasonally perturbed prey-predator system with the Beddington-DeAngelis functional response is studied analytically and numerically. Mathematical theoretical works have been pursuing the investigation of uniformly persistent, which depicts the threshold expression of some critical parameters. Numerical analysis indicates that the seasonality has a strong effect on the dynamical complexity and species biomass using bifurcation diagrams and Poincaré sections. The results show that the seasonality in three different parameters can give rise to rich and complex dynamical behaviors. In addition, the largest Lyapunov exponents are computed. This computation further confirms the existence of chaotic behavior and the accuracy of numerical simulation. All these results are expected to be of use in the study of the dynamic complexity of ecosystems.