含两种群的非线性森林病虫害模型的定性分析  

Qualitative analysis of nonlinear model of forest insect pests with two populations

作　　者：董玉香[1] 王定江[1] 

机构地区：[1]浙江工业大学理学院,浙江杭州310032

出　　处：《浙江工业大学学报》2010年第1期71-74,共4页Journal of Zhejiang University of Technology

基　　金：国家自然科学基金资助项目(60874122);浙江省自然科学基金资助项目(Y606575)

摘　　要：基于经典的传染病模型,将两种群松墨天牛与松树联系在一起建立一类新的森林病虫害系统模型.给出系统的临界阈值的表达式.运用Routh-Hurwitz判据研究了两种群系统模型的动力学性质.证明了当临界阈值小于1时,无病平衡点是局部渐近稳定的,进一步利用巴尔巴欣公式构造Lyapunov函数,运用Lyapunov稳定性理论证明了该平衡点的全局渐近稳定性,说明松材线虫病会最终消失;当临界阈值大于1时,病虫害平衡点是局部渐近稳定的.选取适当的Dulac函数,利用Bendixson-Dulac判别法证明了极限环的不存在性,说明局部渐近稳定的病虫害平衡点也全局渐近稳定.Based on the classical epidemic model, a new forest epidemic model in which the Monochamus Alternatus Hope is linked with Pine tree is established. The expression of the critical threshold is presented. Dynamical property of the system model with two populations is studied based on Lyapunov stability theorem and Routh-Hurwitz criterion. It is proved that, when the value of critical threshold less than 1, the disease-free equilibrium point is globally asymptotically stable. Further more, Bursaphelenchus Xylophilus is used to construct the Lyapunov function, and the stability theory of Lyapunov function is used to prove that the equilibrium point is Global asymptotic stable. It explains that the Bursaphelenchus Xylophilus wiil eventually disappear, when the value of critical threshold larger than 1, the disease and insect pests equilibrium point is locally asymptotically stable An appropriate Dulae function should be choosed and Bendixson-Dulac creterion is used to prove that the limit cycle in this model does not exist. It explains that the disease and insect pests equilibrium point is globally asymptotically stable.

关 键 词：森林 病虫害 临界阈值 全局渐近稳定 极限环 

分 类 号：O175.5[理学—数学]