ABSTRACT
What are Delay Differential Equations (DDE)? is the first question that comes to mind, when you begin reading this chapter. In layman’s terms, a DDE is a differential equation in which the derivatives of some unknown functions at present time are dependent on the values of the functions at previous times. Let us consider a general DDE of the form
dx(t)
dt = f(t, x(t), x(t − τ))
where x(t − τ) = {x(τ) : τ ≤ t} gives the trajectory of the solution in the past. Here, the function f is a functional operator from ×n×C1 to n and x(t)∈ n. We will not provide a detailed discussion on DDEs that fall into the class of functional differential equations. Interested readers are advised to consult references [45, 71, 78].
