Friday, March 16, 2007

3D Discrete Dynamical Systems


































Shown above are 3D scatter plots of several trajectories for a saddle point origin. The program is written in C, based on an old computer graphics project. The L triplet denotes the eigenvalues used to generate the system.

3 comments:

Kea said...

Oooo, fun toy. How's your paper coming along?

Doug said...

The use of "trajectories" with "saddle points" immediately raises the possibility of 'Dynamic Noncooperative Game Theory' by T Basar and GJ Olsder from my perspective.

The above is being extended by 'Max Plus Algebra' of Stephane Gaubert and others [T Basar, GJ Olsder, WM McEneaney, etc] to DES [Discrete Event Systems].

http://www-rocq.inria.fr/MaxplusOrg/

http://arxiv.org/abs/math.OC/0609243

http://www.math.ucsd.edu/~wmcenean/pubs/

kneemo said...

Thanks doug,

Yes, the math.OC/0609243 paper discusses the discrete time version of the max-plus analogue of the spectral equation. Apparently Maslov, Kolokoltsov, and others are members of the idempotent analysis school. This is the approach I take.