The asymptotics of solutions of singularly perturbed functional differential equations: Distributed and concentrated delays are different

This paper illustrates the differences between systems with distributed delays and systems having only concentrated delays in what concerns the asymptotic rates of solutions of singularly perturbed linear retarded functional differential equations. An example of a system with distributed delays shows that the introduction of a “slow” variable coupled with the “fast” variable may decrease the asymptotic rates of solutions observed when the perturbation parameter is close to zero. Such a situation cannot happen for ordinary differential equations, or even for differential-difference equations.