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.
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.