Practicum 1, March 2,
2010,
14:00-16:00

1. I**nstall your personal copy of the MATLAB solver for
Filippov systems:**

** **(a) copy the file FilippovSim.zip
to the Desktop.**
**

(b) unzip the just copied file (right-click on
it and select WinZip -> Extract to
here). The folder FilippovSim will
be created that contains all necessary files.

(c) start MATLAB by selecting Start -> All Programs -> MATLAB ->
R2009a
-> MATLAB R2009a and choose
FilippovSim to be your current folder.

(d) add the current folder to MATLAB Path (via File -> Set Path -> Add Folder).

2. Study the Relay Feedback Example:

(a) examine files in the subfolder RelayFeedback; consult - if
necessary - SECTION 4.1 and APPENDIX A in the paper by Piiroinen & Kuznetsov
(2008).

(b) run MATLAB script run_relay.m in the subfolder RelayFeedback to reproduce Fig.5 of
that paper.

(c) reproduce the right panel of Fig.6 there.

3. Use the solver to simulate other Filippov systems**:**

(a) verify that a Filippov system given in Section 3.2.4 of the
paper by Kuznetsov, Rinaldi
& Gragnani
(2003) has the bifurcation diagram equivalent to II_2 in Fig.12 of that
paper.

(b) simulate the dry-friction oscillator
studied in Section 6.1 of the paper by Dercole
& Kuznetsov (2005) and reproduce phase portraits in Fig.8 of
that paper.