一类具有时滞的森林资源模型的动力学性质分析  

The dynamics of a forest resource model with delay

作　　者：刘立芹[1] 张春蕊[1] LIU Liqin;ZHANG Chunrui(College of Science,Northeast Forestru University,Harbin 150044,China)

机构地区：[1]东北林业大学理学院,哈尔滨100040

出　　处：《黑龙江大学自然科学学报》2020年第2期134-143,共10页Journal of Natural Science of Heilongjiang University

基　　金：中央高校基本科研业务费专项资金项目(2572019BC12)。

摘　　要：考虑一类具有单时滞的延迟森林资源模型的动力学行为。通过将时滞作为分支参数,分析了系统在正平衡点处的线性化系统的特征方程,研究了系统的线性稳定性和Hopf分支的存在性,并且利用中心流形和规范型理论给出了分支方向和分支周期解的稳定性。利用数值模拟验证了所得结论。The dynamics of a forest resource model with a single delay are considered.By regarding the delay as the bifurcation parameter and analyzing the characteristic equation of the linearized system of the system at the positive equilibrium,the linear stability of the system is investigated and Hopf bifurcations are demonstrated.In particular,the direction of the bifurcations and the stability of the bifurcating periodic solutions are given by using the normal form theory and center manifold theorem.A numerical example is given to illustrate the validity of the theoretical results.

关 键 词：森林资源模型 时滞 稳定性 HOPF分支 

分 类 号：O175.1[理学—数学]