Excitability of a second-order delay differential equation

The properties of the equation x′(t)-a2x(t) = bx([t-1]), b≠0 whose coefficients are real constants and [·] denotes the greatest integer function are analyzed. The study continues earlier work on differential equations with piecewise constant arguments (EPCA). Research in this direction is motivated by the fact that EPCA represent a hybrid of continuous and discrete dynamical systems and combine the properties of both differential and difference equations. An attempt is made to extend the theory of functional differential equations with continuous arguments to differential equations with discontinuous arguments.