摘要
讨论了具有非单调传染率的森林病虫害模型.首先证明了无病平衡点和地方病平衡点的存在性,给出了基本再生数R_0,同时当R_0<1时,运用Lyapunov泛函,证明了无病平衡点是全局渐进稳定的,接着,利用Lyapunov-LaSalle不变集原理证明了,当R_0=1时,无病平衡点是全局吸引的;其次,考虑适当的Lyapunov泛函,证明了地方病平衡点是局部渐进稳定的;最后,利用Matlab模拟已验证模型中结论的正确性.
The paper discusses a model of forest insect pests with nonmonotonic incidence rate. Firstly, we proved the existence of disease-free equilibrium point as well as endemic equilibrium point, and derived the basic reproductive number. Uti- lizing Lyapunov functional, the disease-free equilibrium point is globally asymptoti- cally stable, thenthe global attractivity of disease-free equilibrium point is demonstrated usingLyapunov-LaSalle invariance principle. Secondly, considering the proper Lyapunov functional, we further proved the local asymptotically stability of endiemic equilibrium point. Finally, we determined the appropriate values for numerical simulation with Mat- lab, coincident with the conclusion of the theory.
出处
《生物数学学报》
2013年第2期211-219,共9页
Journal of Biomathematics
基金
supported by National Natural Science Foundation(60874122
61273016) of China
关键词
病虫害模型
平衡点
稳定性
LYAPUNOV泛函
数值模拟
Model of forest insect pests
Equilibrium point
Stability
Lyapunov functional
Numerical simulation
