Integral manifolds, stability, and bifurcation of solutions of singularly perturbed functional-differential equations
The integral manifolds and stability zero solution of the system \[ \dot x(t)=F(t,x(t),y_ t),\quad \epsilon \dot y(t)=G_ 1(t,x(t),y_ t), \] where \(x(t)\in {\mathbb{R}}^ m\), \(y(t)\in {\mathbb{R}}^{\ell}\), \(y_ t(\theta)=y(t+\theta)\), -\(\epsilon\Delta\leq \theta \leq 0\) are investigated. The bifurcation of the solution of the system \[ \dot x(t)=\xi x(t)+\eta y(t)\to \zeta y(t-\epsilon \Delta)+F(x(t),y(t),y(t- \epsilon \Delta)) \] \[ \epsilon \dot y(t)=By(t)+Cy(t-\epsilon \Delta)+Dx(t)+G(x(t),y(t),y(t-\epsilon \Delta)) \] is also studied.
scientific article; zbMATH DE number 4000433