Hopf Bifurcation of Rayleigh Model with Delay

Hopf bifurcation and stability of Rayleigh model with delay r as parameter have been studied. Analyzing the stability of zero solution, the branch value of Hopf bifurcation has been obtained. Secondly, using theories of normal form and center manifold acquire the calculation formula of the direction of the bifurcation and the stability of the periodic solution. Finally, some numerical simulations are carried out by using MATLAB software, and the results are consistent with analysis results.