nonlinearity

Laboratory experiments were conducted for a sand layer placed in the vertically­oscillated containers of various shapes. Radial patterns on the sand surface were observed; experimental investigations of such structures have never been described in scientific literature. The waveform, amplitude and frequency of vibrations and the depth of the vibrated layer could be varied, allowing study the dependence of the shape and scale of radial structures upon these parameters.

A continual model of tissue blood supply has been suggested in this paper providing the existence of autostructures in the inhomogeneous blood distribution. Theoretical analysis including both analytical and numerical calculations has been carried out on the base of this model. The filtration variations of blood flow caused by medium activity (chemical reactions, nerve excitation) have been studied as well as self­organization processes accounting mechanisms of microvessel regulation.

Sergei P. Kurdyumov (1928–2004) and his distinguished contribution in the development of the modern interdisciplinary theory and methodology of study of complex self-organizing systems, i.e. synergetics, is under consideration in the article. The matter of a mathematical model of evolutionary dynamics of complex systems elaborated by him is demonstrated. The nonlinear equation of heat conductivity serves as a basis of the model.