#### Schedule for Research Projects

New Students [ Vivek Kumar & Nitin, Sreelakshmi ]

Report 1. 10 marks. Due Wed 6th Feb, 4pm
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. Hand in your code.

Report 2. 10 marks. Due Wed 20th Feb, 4pm [2 weeks]
For the same system as in Report 1:
1. Analyse local stability using the Nyquist Stability Criteria.
2. Analyse local rate of convergence: analytically and numerically.
Identify regions of non-oscillatory and/or oscillatory convergence.

Report 3. 10 marks. Due Wed 6th Mar, 4pm [2 weeks]
From now on, work on the problem that you have been given:
Analyse local stability: sufficient conditions, as well as necessary and sufficient conditions.
Use time domain and/or frequency domain techniques. Plot associated stability charts.

Report 4. 10 marks. Due Wed 27th Mar, 4pm [3 weeks]
Analyse local Hopf bifurcation. Identify if any other bifurcation can take place?
Use the delay, model parameters and a non-dimensional parameter as the bifurcation parameter.
Draw bifurcation diagrams.

Report 5. 10 marks. Due Wed 17th Apr, 4pm [3 weeks]
Analyse local rate of convergence: analytically and numerically.
Identify regions of oscillatory and/or non-oscillatory convergence.
Negative marking will apply. Late submissions will not be accepted.

Report 6. 10 marks. Due Tue 30th Apr, 4pm [2 weeks]
Analyse stability of the local Hopf bifurcation.
Negative marking will apply. Late submissions will not be accepted.

Old Students [ The Rest ]

Draft 1. XX marks. Due Fri 1st Feb, 4pm
1. Do Abstract and General of Guidelines. Give a print out of whole paper. Put Abstract in Google Docs.
2. Do Stage 6 of Guidelines for Research Reports. Order the journals in Google Docs.
Give a print out, of the scope, of the suitable journal(s).

Draft 2. XX marks. Due Wed 6th Feb, 4pm
1. Do Abstract, Introduction, Conclusion, General of Guidelines
2. Do Stages 2,3,5,6 of Guidelines for Research Reports
3. Print out of your paper in the format of the pertinent journal.
Print out of the original paper(s) where the model was derived.

Draft 3. XX marks. Due Thur 28th Feb, 4pm
I expect a version that you will be happy to submit for peer-review publication.

Draft 4. 15 marks. Due Mon 15th April, 4pm
I expect a version that you will be happy to submit for peer-review publication.
Negative marking will apply. Late submissions will not be accepted.

Final Version. 30 marks. Due Tue 30th April, 4pm
Negative marking will apply. Late submissions will not be accepted.