Reference request for an introduction to delay differential equations.

Question

I am currently taking a course in delayed differential equations (DDEs) and I am finding the instructor's notes too narrow/hard to follow. I am looking for for good textbooks/papers in different topics including:

1. An general introduction to DDEs.
2. Solving DDEs using the methods of steps.
3. The conditions for the positivity of solutions to DDEs.
4. Using Lyapunov functionals to determine stability.
5. Using characteristic equations to determine stability.
6. Numerical methods for DDEs.
7. Hopf Bifurcation for DDEs.

Note: It would be great if in your answer to this question you use the numbers above to indicate which reference(s) cover which topic(s).

Answer 1

Probably the most basic treatment of delay differential equations is contained in Introduction to the theory and application of differential equations with deviating arguments by Elsgolts. I am not sure how easy to get hold of this book though.

Your list is somewhat more involved and actually Hall Smith recently published a book that fits most of your points (no treatment of numerical algorithms as I recall): An Introduction to Delay Differential Equations with Applications to the Life Sciences

Since the OP asked for something more involved, I would like to recommend

• Delay Differential Equations: With Applications in Population Dynamics by Kuang.

If this still not advanced enough two classics are, of course,

• Theory of Functional Differential Equations by Jack Hale
• Delay Equations: Functional-, Complex-, and Nonlinear Analysis by Dieckmann et al.

But these two books (as far as I can recall) suppose good background in functional analysis.