Hopf bifurcation and stability of periodic solutions for van der Pol equation with time delay
Consider the van der Pol equation with delay \[ \dot x(t)= y(t-\tau)- ax(t-\tau)- b(x(t- \tau))^2, \] \[ \dot y(t)=- x(t-\tau). \] The authors study Hopf bifurcation of the origin with \(\tau\) as bifurcation parameter in dependence on the parameter \(a\). By means of a center manifold and a normal form they determine the bifurcation direction and the stability of the bifurcating periodic solution.
scientific article; zbMATH DE number 2183190