My professor agreed to get me as her research assistant. She asked me to use DDE-biftool in Matlab to find computation of steady state and computation of stability etc. Some examples of the work can be found here.
My problem is, which the Professor also realizes that I am yet to do courses on Ordinary Differential Equation or Dynamical Systems. So I do not have the basic knowledge of how such analysis takes place.
I hope someone might be able to advise me on how to go forward with this. I do not have problem reading textbooks and teaching myself, but the amount of time I can invest is limited. I wanted to read the Elementary Differential Equation book however, I am not sure if I need to read every chapter or not.
Thank you.
If you have absolutely no background in ODE's, reading Strogatz's "Nonlinear Dynamics and Chaos" coupled with any standard ODE textbook is the most accessible and elementary introduction to bifurcation theory you'll find.
For a more advanced reading into bifurcation theory and nonlinear dynamics that includes delay differential equations with a focus on oscillations, I'd recommend Rand's "Lecture Notes on Nonlinear Vibrations".