【摘要】 在Neumann边值条件下，研究带有扩散和中立项的Nicholson果蝇模型的Hopf分支.首先，将时滞τ作为分支参数，研究唯一的正常值稳态解的稳定性及Hopf分支的存在性.其次，利用中心流形及规范型的相关方法与理论，分析Hopf分支的方向和分支周期解的稳定性.最后，利用数值模拟验证所得的结论.更多还原

【Abstract】 Hopf bifurcation of a Nicholson’s blowflies model with diffusion and neutral terms is investigated under Neumann boundary condition. Firstly, by taking the time delay as a bifurcation parameter, the stability of unique positive steady state and the existence of Hopf bifurcation are discussed. Secondly, by using the relevant theories of the central manifold and normal forms, we analyze the direction of Hopf bifurcation and the stability of periodic solutions. At last, numerical simulations are performed to verify the validity of the analytical results.更多还原