Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Dynamics of a Predator-Prey System Concerning Biological and Chemical Controls | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 598495 17 pages doi 2010 598495 Research Article Dynamics of a Predator-Prey System Concerning Biological and Chemical Controls Hye Kyung Kim1 and Hunki Baek2 1 Department of Mathematics Education Catholic University of Daegu Kyongsan 712-702 Republic of Korea 2 Department of Mathematics Kyungpook National University Daegu 702-701 Republic of Korea Correspondence should be addressed to Hunki Baek hkbaek@ Received 25 August 2010 Accepted 13 November 2010 Academic Editor Mohamed A. El-Gebeily Copyright 2010 H. K. Kim and H. Baek. 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 investigate an impulsive predator-prey system with Monod-Haldane type functional response and control strategies especially biological and chemical controls. Conditions for the stability of the prey-free positive periodic solution and for the permanence of the system are established via the Floquet theory and comparison theorem. Numerical examples are also illustrated to substantiate mathematical results and to show that the system could give birth to various kinds of dynamical behaviors including periodic doubling and chaotic attractor. Finally in discussion section we consider the dynamic behaviors of the system when the growth rate of the prey varies according to seasonal effects. 1. Introduction In recent years controlling insects and other arthropods has become an increasingly complex issue. There are many ways that can be used to help control the population of insect pests. Integrated Pest Management IPM is a pest control strategy that uses an array of complementary methods natural predators and parasites pest-resistant varieties cultural practices biological controls various physical techniques and the strategic .
