Local dynamics of nonlinear singularly perturbed delay systems (Q2703892)

Here, the singularly perturbed delay differential equation is considered: NEWLINE\[NEWLINE\varepsilon\dot x(t)=A (\varepsilon)x(t)+ B(\rho,\varepsilon) x(t-1)+ F\bigl(x(t), x(t-1)\bigr),\;x(t)\in\mathbb{R}^n,NEWLINE\]NEWLINE with \(A(\varepsilon)= A+ \varepsilon A_1\), \(B(\rho,\varepsilon) =\rho B+ \varepsilon B_1\), \(\varepsilon> 0\), \(\rho>0\). The dynamics of the system in a small neighborhood of an equilibrium and some critical cases are investigated. New effects are discovered.