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 Optimal Harvest of a Stochastic Predator-Prey Model | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 312465 18 pages doi 2011 312465 Research Article Optimal Harvest of a Stochastic Predator-Prey Model Jingliang Lv1 and Ke Wang1 2 1 Department of Mathematics Harbin Institute of Technology Weihai Weihai 264209 China 2 School of Mathematics and Statistics Northeast Normal University Changchun 130024 China Correspondence should be addressed to Jingliang Lv yxmliang@ Received 12 January 2011 Accepted 20 February 2011 Academic Editor Toka Diagana Copyright 2011 J. Lv and K. Wang. 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 firstly show the permanence of hybrid prey-predator system. Then when both white and color noises are taken into account we examine the asymptotic properties of stochastic prey-predator model with Markovian switching. Finally the optimal harvest policy of stochastic prey-predator model perturbed by white noise is considered. 1. Introduction Population systems have long been an important theme in mathematical biology due to their universal existence and importance. As a result interest in mathematical models for populations with interaction between species has been on the increase. Generally many models in theoretical ecology take the classical Lotka-Volterra model of interacting species as a starting point as follows dp diag x1 f . x f b Ax f where x i x1ft . xnft T b bi 1x and A ữij nxn. The Lotka-Volterra model has been studied extensively by many authors. Specifically the dynamics relationship between predators and their preys also is an important topic in both ecology and mathematical ecology. For two-species predator-prey model the population model has the form ddd x t U1 - b1 x D - C1y t d did yd a2 - b2y t c2x f 2 Advances in Difference Equations where x t y t
