In this paper,we consider the long-term sustainability of the northeast Korean pine.We propose a class of natural Korean pine population system with time delay and diffusion term.First,by analyzing the roots distribut...In this paper,we consider the long-term sustainability of the northeast Korean pine.We propose a class of natural Korean pine population system with time delay and diffusion term.First,by analyzing the roots distribution of the characteristic equation,we study the stability of the model system with diffusion terms and prove the occurrence of Hopf bifurcation.Second,we introduce lactation time delay into a population model with a diffusion term,based on stability theory of ordinary differential equation,norm form methods and center manifold theorem,the stability of bifurcating periodic solutions and the relevant formula for the direction of Hopf bifurcation are given.Finally,some numerical simulations are given.展开更多
基金supported by the National Natural Science Foundation of China(No.11201095)the Fundamental Research Funds for the Central Universities(No.3072022TS2402)+1 种基金the Postdoctoral research startup foundation of Heilongjiang(No.LBH-Q14044)the Science Research Funds for Overseas Returned Chinese Scholars of Heilongjiang Province(No.LC201502).
文摘In this paper,we consider the long-term sustainability of the northeast Korean pine.We propose a class of natural Korean pine population system with time delay and diffusion term.First,by analyzing the roots distribution of the characteristic equation,we study the stability of the model system with diffusion terms and prove the occurrence of Hopf bifurcation.Second,we introduce lactation time delay into a population model with a diffusion term,based on stability theory of ordinary differential equation,norm form methods and center manifold theorem,the stability of bifurcating periodic solutions and the relevant formula for the direction of Hopf bifurcation are given.Finally,some numerical simulations are given.
