Modelling of chaotic processes

COURSE DESCRIPTION

The basic ideas of the course are presented through the analysis of one-dimensional iterative circuits in situations where their behaviour becomes chaotic. Fractals, attractors, bifurcations and other chaos quantities are explained. The knowledge gained will be applied to the understanding of chaotic cryptography techniques, fractal compression of digital images and the basic ideas of modelling chaotic objects and processes.

CONTENT

1. Continuous and discrete modelling
2. World predictability
3. Butterfly effect
4. Periodic trajectories
5. Logistical and tent scheme
6. Bifurcations of the logistic scheme
7. The fractal dimension
8. Chaos in continuous systems
9. Chaos in oscillating systems
10. Van der Pohl oscillator
11. Chaotic encryption of signals
12. Chaos formation scenarios
13. Static (object) modelling
14. Dynamic (process) modelling
15. Image fractal compression