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- Introduction: goals and purposes of synergetics, some typical problems and examples.
- Probability: sample space, random variables, probability, random variables, probability distributions, expectation and moments, random processes, empirical estimation, empirical modeling.
- Information: information entropy, principle of maximal entropy, estimation of probability distribution from empirical data.
- Chance: model of Brownian movement, master equation, Markov processes, fluctuations.
- Necessity: dynamic processes, critical points, limit cycles, stability, bifurcations.
- Chance and necessity: Langevin equations, Fokker-Planck equation, phase transition analogy.
- Self-organization: organization, self-organization, the role of fluctuations and order parameters, ordered structures and patterns.
- Physical systems: lasers, instabilities in fluid dynamics, elastic stability, instabilities in mechanical processes, reaction and population instabilities.
- Deterministic chaos: nonlinear dynamic systems, phase space, attractors, Fourier spectrum, Poincare mapping, ways to chaos, period dubling, bifurcation diagrams, transient chaos, conservative chaos, Lyapunov exponents, fractal dimension, modeling and prediction of chaotic time series.
- Automatic modeling of natural phenomena: inteligent self-organizing systems, neural networks, optimal estimators, control of technical processes.