About this Journal Submit a Manuscript Table of Contents
Advances in Mathematical Physics
Volume 2014 (2014), Article ID 375236, 10 pages
http://dx.doi.org/10.1155/2014/375236
Research Article

Effects of Behavioral Tactics of Predators on Dynamics of a Predator-Prey System

1Department of Applied Mathematics, School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi'an, Shaanxi 710027, China
2Institute of Bioinformatics, School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
3School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi 710027, China
4School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Received 8 April 2014; Accepted 11 May 2014; Published 26 May 2014

Academic Editor: Xiao-Jun Yang

Copyright © 2014 Hui Zhang 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.

Abstract

A predator-prey model incorporating individual behavior is presented, where the predator-prey interaction is described by a classical Lotka-Volterra model with self-limiting prey; predators can use the behavioral tactics of rock-paper-scissors to dispute a prey when they meet. The predator behavioral change is described by replicator equations, a game dynamic model at the fast time scale, whereas predator-prey interactions are assumed acting at a relatively slow time scale. Aggregation approach is applied to combine the two time scales into a single one. The analytical results show that predators have an equal probability to adopt three strategies at the stable state of the predator-prey interaction system. The diversification tactics taking by predator population benefits the survival of the predator population itself, more importantly, it also maintains the stability of the predator-prey system. Explicitly, immediate contest behavior of predators can promote density of the predator population and keep the preys at a lower density. However, a large cost of fighting will cause not only the density of predators to be lower but also preys to be higher, which may even lead to extinction of the predator populations.