Asymptotic study of the corporate dynamics of systems of equations coupled by delay control (Q1760968)

Consider the singularly perturbed differential-delay system \[ \begin{aligned} \varepsilon{du\over dt} &=\varepsilon F(u)+ v(t- h)- u,\\ \varepsilon{dv\over dt} &=\varepsilon G(v)+ u(t- h)- v.\end{aligned}\tag{\(*\)} \] The main concern of the author is to derive some boundary value problem for a system of parabolic differential equations not depending on the small parameter \(\varepsilon\) which determines the dynamics of system \((*)\) for sufficiently small \(\varepsilon\). The paper contains no proofs of the formulated results.