具有时滞的植物传染病模型的稳定性和Hopf分支  

Stability and Hopf bifurcation of a plant epidemic model with time delays

作　　者：万槟萁 刘俊利[1] WAN Binqi;LIU Junli(School of Science,Xi′an Polytechnic University,Xi′an 710048,China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《纺织高校基础科学学报》2018年第2期164-171,203,共9页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(11101323);陕西省自然科学基础研究计划项目(2014JQ1038);陕西省教育厅专项科研计划项目(16JK1331)

摘　　要：研究一类依赖昆虫媒介传播的具有时滞的植物传染病模型.若基本再生数R0≤1,模型仅存在唯一的无病平衡点,利用Routh-Hurwitz判据讨论无病平衡点的局部渐近稳定性,构造Liapunov泛函方法讨论无病平衡点的全局渐近稳定性.若基本再生数R0>1,无病平衡点不稳定,模型还存在唯一的正平衡点,进一步讨论正平衡点处的局部稳定性和Hopf分支的存在性,并用中心流形定理和正规型理论确定了分支周期解的稳定性和分支方向.最后通过数值模拟验证了理论分析的正确性.A class of plant epidemic model dependence on insect vector transmission with time delays was studied.When the basic reproduction number R 0≤1,the only disease-free equilibrium exists,by using Routh-Hurwitz criteria and Liapunov functional methods,the global stability of the disease-free equilibrium is obtained.When the basic reproduction number R 0>1,the disease-free equilibrium is unstable,the model has the unique positive equilibrium.Furthermore,the local stability and Hopf bifurcation of the positive equilibrium is also discussed,and the center manifold theorem and the normal form theory are used to determine the stability of bifurcating periodic solutions and the direction of bifurcation.The numerical simulation results verify the correctness of the theory analysis.

关 键 词：基本再生数 全局稳定性 LIAPUNOV泛函 HOPF分支 中心流形定理 

分 类 号：O175.14[理学—数学]