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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 358930, 15 pages
http://dx.doi.org/10.1155/2013/358930
Research Article

Complex Dynamical Behaviors in a Predator-Prey System with Generalized Group Defense and Impulsive Control Strategy

Department of Mathematics, Qiannan Normal College for Nationalities, Duyun, Guizhou 558000, China

Received 1 November 2012; Accepted 20 May 2013

Academic Editor: Patricia J. Y. Wong

Copyright © 2013 Shunyi Li. 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.

Abstract

A predator-prey system with generalized group defense and impulsive control strategy is investigated. By using Floquet theorem and small amplitude perturbation skills, a local asymptotically stable prey-eradication periodic solution is obtained when the impulsive period is less than some critical value. Otherwise, the system is permanent if the impulsive period is larger than the critical value. By using bifurcation theory, we show the existence and stability of positive periodic solution when the pest eradication lost its stability. Numerical examples show that the system considered has more complicated dynamics, including (1) high-order quasiperiodic and periodic oscillation, (2) period-doubling and halving bifurcation, (3) nonunique dynamics (meaning that several attractors coexist), and (4) chaos and attractor crisis. Further, the importance of the impulsive period, the released amount of mature predators and the degree of group defense effect are discussed. Finally, the biological implications of the results and the impulsive control strategy are discussed.