Here you can see the examples of images that DEREK can build in the analysis of dynamical systems
Phase portrait (projection on the plane)
Dependence of the first component on the time
One of the possible trajectories of an artificial satellite in the gravity field of the Earth and Moon
Quasi-periodic motion, shown with the points of Poincaré section for the plane x + y + z = 0
Chaotic motion, shown with the points of Poincaré section for the plane x + y + z = 0
Periodic chemical reaction (phase trajectory forms a limit cycle)
Model of chemical reactions ("stiff" system)
Motion of charged particles in a magnetic field of the Earth (for the description of "Northern Lights"-Aurora borealis)
Case F
The dependence of the Lyapunov exponents on the parameter for the Lorenz model
Editing the description of the system in a DEREK database of dynamical systems
Three-dimensional image of Rössler attractor
Three-dimensional image for motion of Henon-Heiles model with the points of the Poincaré section
quasi-periodic motion
chaotic motion
If you will not be frightened with a few number of formulas you can refer to the Experiments page, several examples are presented there in more detail.