Research Article The Effects of Resource Limitation on a Predator-Prey Model with Control Measures as Nonlinear Pulses Wenjie Qin, 1 Sanyi Tang, 1 and Robert A. Cheke 2 1 College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China 2 Natural Resources Institute, University of Greenwich at Medway, Kent ME4 4TB, UK Correspondence should be addressed to Wenjie Qin; wenjieqin@hotmail.com Received 16 October 2013; Accepted 26 January 2014; Published 11 March 2014 Academic Editor: Jui-Sheng Lin Copyright © 2014 Wenjie Qin et al. his 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. he dynamical behavior of a Holling II predator-prey model with control measures as nonlinear pulses is proposed and analyzed theoretically and numerically to understand how resource limitation afects pest population outbreaks. he threshold conditions for the stability of the pest-free periodic solution are given. Latin hypercube sampling/partial rank correlation coeicients are used to perform sensitivity analysis for the threshold concerning pest extinction to determine the signiicance of each parameter. Comparing this threshold value with that without resource limitation, our results indicate that it is essential to increase the pesticide’s eicacy against the pest and reduce its efectiveness against the natural enemy, while enhancing the eiciency of the natural enemies. Once the threshold value exceeds a critical level, both pest and its natural enemies populations can oscillate periodically. Further- more, when the pulse period and constant stocking number as a bifurcation parameter, the predator-prey model reveals complex dynamics. In addition, numerical results are presented to illustrate the feasibility of our main results. 1. Introduction It is well known that pest outbreaks oten cause serious eco- logical and economic problems, requiring complex control measures to reduce harm due to insect pests of agriculture and insect vectors of important plant, animal, and human diseases. Such measures include use of a variety of chemical pesticides, biological pesticides, and biological control. Biological control is the reduction of pest populations by other living organisms, oten called natural enemies or beneicial species (see [1–3]). Virtually all pests have some natural enemies, and the key to successful pest control is to identify the pest and its main natural enemies and to release the beneicial insects early when pest levels are low. Chemical control relies mainly on the use of synthetic pesticides to suppress pests. Pesticides are useful because they quickly kill a signiicant portion of a pest population and they sometimes provide the only feasible method for preventing economic loss. However, pesticide pollution is also recognized as a major health hazard to people and to pest’s natural enemies. Also, overuse of a single control tactic is discouraged to avoid or delay the development of resistance by the pest to the control tactic, to minimize damage to nontarget organisms, and to preserve the quality of the environment. herefore, it is natural to combine biological and chemical controls as components of integrated pest management (IPM). he concept of IPM was introduced in the late 1950s [4], was widely practised during the 1970s and 1980s [5], and is still oten adopted. IPM emphasizes the importance of interactions between pests and its natural enemies and is a long-term management strategy to reduce pests to predeter- mined economic injury levels, with little cost and minimal efects on the environment. IPM has been shown to be more efective than the traditional methods, such as biological control or chemical control alone, both experimentally [6, 7] and theoretically [8, 9]. hese results indicate that diferent pest control techniques should work together rather than against each other. In the last few decades, in order to consider the con- sequences of spraying pesticides and introducing additional predators into a natural predator-pest system, many authors have suggested impulsive diferential equations to investigate Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2014, Article ID 450935, 13 pages http://dx.doi.org/10.1155/2014/450935