NONLINEAR OSCILLATIONS AND DISSIPATIVE STRUCTURES (A.A.Polezhaev)
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- Basic concepts
- Open systems, non-equilibrium states, thermodynamics of open systems
- Subordination principle
- Active media, autovawes, dissipative structures
- Elements of qualitative theory of dynamical systems
- Phase portrait, trajectory, basic types of bifurcations in a plane
- Characteristic Lyapunov exponents
- Concept of attractor, strange attractors
- Puancare map
- Bifurcations in multidimensional systems, chaos in dynamical systems and scenarios (ways) of its appearance
- Fractal structures and their dimension
- Autowave structures
- Models of excitable media
- Systems with multiple stationary states
- Autowave regimes in media with diffusion, displacement waves, traveling pulses, spiral waves.
- Target patterns
- Theory of stationary dissipative structures
- Dissipative structures, turing bifurcation
- Sharp and quasi-harmonic DS
- Construction of DS solutions near the Turing bifurcation
- Method of construction of sharp DS
- Spatial-temporal patterns in physical and chemical systems
- The Prigogine-Lefevr-Nicolis model (Brusselator)
- Belousov-Zhabotinsky reaction, Fild-Noice model (Oregonator)
- Hydrodynamic instabilities, the Benard effect
- Autowave media in solid matter.
- Heat waves and non-uniform stationary states
- Self-organization in biological systems
- The pronlem of biological self-organization
- The concept of biological (morphological) field, positional information
- The role of DS in morphogenesis, chemical basis of morphogenesis
- Morphogenesis of hydra, the Gierer-Mainhardt model
- Mechanism of pattern formation on animal skins, morphogenesis in insects
- The role of currents in processes of self-organization
- Models of mechanisms of pattern formation in bacterial colonies and Dictyostellium Discoideum amoebae
- "Mechanical" models of morphogenesis
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