Instability

Systems with delays are only mathematical models of some real processes with aftereffect, so, generally speaking, we should consider initial functions to be some functions that occur in practice. However for different real processes there can be different admissible initial functions, and it would be reasonable to consider initial value problem only for admissible initial conditions. But this would be a formal theory, because we do not know admissible initial functions a priori and besides a set of initial functions can have a complicated structure.