460-6020/01 – Modeling and Simulation of Complex Systems (MaSKS)
| Gurantor department | Department of Computer Science | Credits | 10 |
| Subject guarantor | prof. Ing. Ivan Zelinka, Ph.D. | Subject version guarantor | prof. Ing. Ivan Zelinka, Ph.D. |
| Study level | postgraduate | Requirement | Choice-compulsory |
| Year | | Semester | winter + summer |
| | Study language | Czech |
| Year of introduction | 2014/2015 | Year of cancellation | |
| Intended for the faculties | FEI | Intended for study types | Doctoral |
Subject aims expressed by acquired skills and competences
The aim of the course is to acquaint the students with the problems of complex systems and mathematical modeling to implementation on computers. The course will discuss various interesting areas of complex systems emphasizing their mathematical-physical-algorithmic description and subsequent simulation on PC. The course will give students an interdisciplinary field of HPC view on the issue of complex systems, their inherent parallelism and dynamic behavior. Graduate get an overview of modern computational procedure allowing to model and simulate the otherwise very complicated and complex systems. After successfully completing the course will have an interdisciplinary graduate survey knowledge of complex systems and be able to apply the methods discussed in the course to real problems. Students should be able to further deeper self in this issue.
Teaching methods
Individual consultations
Summary
In this course will discuss a wider range of complex systems and their behavior. They discussed how mathematical tools and methods for their modeling and simulations on a PC. They discussed such systems as nonlinear systems generating deterministic chaos, the effect of "Self-organized criticality" causing the avalanche effect leading to eventual spontaneous rearrangement of the system. Students will become familiar with the so-called Thom's catastrophe theory and its occurrence in many biological, economic as well as technical systems. There will also be discussed on cellular automata and their behavior, complex networks apod.Velký emphasis will be placed on the practical side of things - the ability to apply most of the discussed methods to practical examples. The student should have after completing the course, a comprehensive knowledge of the above-mentioned areas, including the possibility jeich use. The course includes laboratory exercises in which students will practice how to program the selected algorithms and their application to solving practical problems.
Compulsory literature:
Recommended literature:
4. R. Gilmore 1993, Catastrophe Theory for Scientists and Engineers, John Wiley and Sons, ISBN 0-486-67-539-4, 1993
Way of continuous check of knowledge in the course of semester
The examination is based on the elaboration of the protocols of the subject, by which the student demonstrates not only the understanding of the lecture information but also the ability to implement them in the given programming environment. The exam is oral.
E-learning
Other requirements
Additional requirements are placed on the student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Complexity. The current state of understanding of the issue of complex systems and their classification. Synergetics. Demonstration-motivational examples and videos demonstrating the occurrence of the behavior of complex systems in everyday real life.
2. Fractaln geometry and visualization of complex structures. History, definition of fractals, types of algorithms that generate fractals. Fractal dimension interpolation and compression. Development systems and artificial life. L-systems, turtle graphics, parametric L-systems, L-systems from the perspective of fractal geometry.
3. Deterministic chaos. Historical outline a classification of dynamical systems, generating chaos. Simple models and examples for. Determinism and the edge of chaos (according to Kaufmann). Four typical chaotic systems: predator-prey model Lorenzo weather, electronic and three body problem (binary model and the planet). Divergence of nearby trajectories. Determinism and unpredictability.
4. Invariants of chaotic behavior. Feigenbaum constant, self-similarity, U-sequences, computers and chaos.
5. Deterministic chaos. Discrete dynamical systems. Basic simple models, Poincaré sections, bifurcation, bifurcation diagram as a holistic view of system behavior, examples.
6. Deterministic chaos. Continuous dynamical systems. State space system, singular points and areas of attraction. Models in 2D and 3D. Limit cycles and Poincare sections. Lyapunov exponents and divergence of nearby trajectories.
7. Deterministic chaos. From order to chaos: the path leading to chaotic behavior. Period doubling, quasiperiodicity, intermittence and crisis. Bifurcation and Thom's catastrophe.
8. Deterministic chaos. Analysis of chaotic behavior and methods of reconstruction. Use of the cryptographic techniques of chaos control and its occurrence in economic systems.
9. Thom's catastrophe theory and association with chaotic behavior. Introduction, basic models and hierarchies disasters. Their occurrence in the dynamics of systems and identification of the signs in the data. Examples of occurrence: economic systems, physical systems, mechanical systems.
10. Complex Systems generating effect "Self-organized criticality" (self-organized of Critical - SOC), modeling (models of a pile of sand, ...) a real occurrence in complex systems (evolution, earthquakes, avalanches).
11. Cellular Automata (BA) and complex systems. Introduction, BA formalism, dynamics and classification of cellular automata by Wolfram, Conway's Game of Life, modeling using BA. Cellular automata and spatio-temporal chaos.
12. Comprehensive network. Introduction to the problems of complex networks, visualization methods and algorithms of their dynamics. Examples of the occurrence of complex networks (social networks, the dynamics of evolutionary processes, ...). Visualization of the dynamics of complex networks by using models of chaotic systems.
13. Neural Network (ANN). History and basic principles NS. Training set and use NS. Basic types of networks and their applications to different types of problems. Evolutionary cultivated large neural networks, their non-standard structure, demonstrating the occurrence of chaotic regimes in neural networks.
14. Evolutionary process as a complex system. Their dynamics and visualization. Summarization and end of the course.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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