tailieunhanh - báo cáo hóa học:" Research Article Dynamical Analysis of a Delayed Predator-Prey System with Birth Pulse and Impulsive Harvesting at Different Moments"

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 Dynamical Analysis of a Delayed Predator-Prey System with Birth Pulse and Impulsive Harvesting at Different Moments | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 954684 15 pages doi 2010 954684 Research Article Dynamical Analysis of a Delayed Predator-Prey System with Birth Pulse and Impulsive Harvesting at Different Moments Jianjun Jiao1 and Lansun Chen2 1 Guizhou Key Laboratory of Economic System Simulation School of Mathematics and Statistics Guizhou College of Finance and Economics Guiyang 550004 China 2 Institute of Mathematics Academy of Mathematics and System Sciences Beijing 100080 China Correspondence should be addressed to Jianjun Jiao jiaojianjun05@ Received 21 August 2010 Accepted 22 September 2010 Academic Editor Kanishka Perera Copyright 2010 J. Jiao and L. Chen. 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 consider a delayed Holling type II predator-prey system with birth pulse and impulsive harvesting on predator population at different moments. Firstly we prove that all solutions of the investigated system are uniformly ultimately bounded. Secondly the conditions of the globally attractive prey-extinction boundary periodic solution of the investigated system are obtained. Finally the permanence of the investigated system is also obtained. Our results provide reliable tactic basis for the practical biological economics management. 1. Introduction Theories of impulsive differential equations have been introduced into population dynamics lately 1 2 . Impulsive equations are found in almost every domain of applied science and have been studied in many investigation 3-11 they generally describe phenomena which are subject to steep or instantaneous changes. In 11 Jiao et al. suggested releasing pesticides is combined with transmitting infective pests into an SI model. This may be accomplished using selecting pesticides and timing the application .