一类具有时滞的Sel’kov模型的Hopf分歧分析

Hopf bifurcation analysis of Sel’kov model with time delay

研究了一类在齐次Neumann边界条件下具有时滞扩散的Sel’kov模型。首先利用谱理论得到了该模型正平衡点的局部渐近稳定性;其次,以时滞为分歧参数,研究了该模型Hopf分歧的存在性;接着根据偏泛函微分方程的中心流形定理和正规型理论,得到了该Hopf分歧周期解的稳定性和分歧方向;最后利用Matlab软件,模拟了该系统在临界点附近经历的Hopf分歧。结果表明,时滞能够影响Sel’kov模型的稳定性。

The Sel’kov model with time-delay diffusion under homogeneous Neumann boundary conditions is considered.Firstly,the local asymptotically stability of the positive equilibrium point of the model is obtained by using spectral theory.Secondly,the existence of Hopf bifurcation of the model is studied by taking the time delay as the bifurcation parameter.Then,according to the central manifold theorem and the normal form theory of partial differential functional equation,the stability and bifurcation direction of the Hopf bifurcation periodic solutions are obtained.Finally,with Matlab software,the Hopf bifurcation experienced by the system near the critical point is simulated.The resulTSshow that the time delay can affect the stability of the Sel’kov model.