Synergetics in Physics

Lectures: 34 hours

Practical studies:  -

Self-instruction:  7 hours

1 master course (1 term)
Course program: 

Introduction. Open non-equilibrium systems. Effects studied in synergetics. Nonlinearity of equations which describe  self-organization of systems.  

Mathematical bases of self-organization.  Dynamic variables. Basic equations for dynamic variables. Phase space and phase  trajectories. Stationary points. Stability. Lyapunov theorems. Normal form of equations. Single degree-of-freedom systems. Two degree-of-freedom systems. Classification of stationary points. Autooscillations. Theorems  about limiting cycle. Structural stability. Bifurcation. Analytical solutions near bifurcation point. Fast and slow movements. Adiabatic approximation. Tihonov theorems. Spatially inhomogeneous systems.  

Static instabilities.   Change of stationary points stability. Loss of fixed column stability. Laser generation. Bistability in chemical reactions. Bistability in electric circuts (trigger). Optical bistability. Conceptions of catastrophe theory. Analogy between equilibrium and nonequilibrium phase transitions.  

Autooscillation processes. Autooscillation in electric circuit. Van der Pol method. Evolution of  “predator-victim”  type systems. Chemical oscillations.  Belousov-Zhabotinsky reaction. Синхронізація автоколивань. Автоколивальна система під дією періодичної сили. Synchronization of coupled generators.  

Dissipative structures. Absence of dissipative strucutures in one-dimensional systems described by second order differential equation. Model of chemical reaction “brusselator”. Benard effect.  

Autowaves.  Traveling edges. Traveling pulses. Domain motion in semiconductots. Gunn effect.  

Stochastic processes.  Markovian processes. Chapman-Kolmogorov equation. Kinetic equation. Fokker-Planck equation. Langevin equation. Stochastic differential equations.  

Deterministic chaos.  Strange attractor. Recognition of chaos.

Knowledge tests: 




1. Cугаков В.Й. Основи синергетики. К., 2001.  

2.Лоскутов А.Ю., Михайлов А.С. Введение в синергетику.- М., 1990.


1. H. Haken. Synergetics.  1977.

2. G. Nicolis, I. Prigogine. Self-organization in nonequilibrium systems. 1977.

3. Эбелинг В. Образование структур при необратимых процессах. - М., Мир, 1979.