Hopf bifurcation analysis of Sel’kov model with time delay

Abstract

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 results show that the time delay can affect the stability of the Sel’kov model.

Keywords

• time delay
• sel’kov model
• hopf bifurcation
• stability
• simulations