### Some Research Guidelines

Stage 1: Getting started
1. Understand Appendix of Local bifurcation analysis of some dual congestion control algorithms
IEEE Transactions on Automatic Control, vol. 50, pp. 1135-1146, 2005.
2. Put Appendix in IEEE style file format [Latex].
3. In Appendix, there is a numerical simulation. Repeat it using XPP [or Matlab, or similar package].
4. In Appexdix, there is a stability chart. Make the plot in R, using psfrag.
5. In Appendix, there are a few examples. Repeat the examples.

Stage 2: Early stages
1. Read Model, modelling and all that stuff
2. Put your model in Latex.

Stage 3: Doing the research
1. Local stability (frequency and/or time domain): sufficient, and necessary & sufficient conditions. Draw stability charts.
2. Analyse local rate of convergence (analytically and/or numerically).
Identify regions of non-oscillatory and/or oscillatory convergence.
3. Characterise the local Hopf bifurcation. Any other bifurcations? Draw bifurcation diagrams.
Use the delay, model parameters and a non-dimensional parameter as the bifurcation parameter.
4. Address the stability of the local Hopf bifurcation.

Stage 4: Advanced research
1. Extend local analysis. Options: global stability, global Hopf, boundedness of solutions, robustness, etc.

Stage 5: Writing the paper
1. Read the following Guidelines to writing a paper.
2. For some ideas, see how this paper is written: Part II: control theory for buffer sizing
ACM Computer Communication Review, vol. 35, pp. 79-82, 2005.

Stage 6: Working towards submission of the paper
1. Identify a journal, after looking at a few possible Journals in [control, nonlinear, applied maths].
In each category [control, nonlinear, maths] order journals, in google docs, accordingly to suitability.

2. Ways to decide on a journal
a) Read the scope of the journal and the guidelines for authors, etc.
b) Download a few papers from the journal to get a sense of the type of papers that get published there.

3. Once you have decided on a specific journal
a) Download 10 papers from the journal, and read them while paying special attention to the abstract, introduction and conclusions.
b) See how the authors have presented their work, in terms of analysis and the numerical work.
c) Look for specific instructions for references for that particular journal.
d) No need to understand others work. Just develop a sense of the format/style/expectations of the journal.