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The analysis of the system behavior under the effect of the additive noises has been done using a simple model of shear melting. The situation with low intensity of the order parameter noise has been investigated in detail, and time dependence of the order parameter has been calculated. A distinctive feature of the obtained dependence is power-law distribution and self-similarity. The generalized Hurst exponent of the time series has been found within multifractal detrended fluctuation analysis. It is shown that the self-similarity of the time series increases when the noise intensity reduces.

A synergetic model describing the state of an ultrathin lubricant layer squeezed between two atomically smooth solid surfaces operating in the boundary friction mode has been developed further. To explain the presence of different operation modes of the system for various sets of its main parameters, the mathematical analysis of the synergetic model is carried out. The type of functioning a tribological system is described in accordance with the stability character of singular points, and the diagrams distinguishing various operation modes are obtained. Phase portraits corresponding to different stability types are plotted for all diagram areas. A stick-slip mode of motion that is often observed experimentally is described.K e y w o r d s: boundary friction, friction force, shear stresses, strange attractor, Lorenz system.

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The synergetic model, that allows representing the processes proceeding at the boundary friction of two atomically smooth surfaces divided by an ultrathin layer of lubricant material is studied. The model is based on the Lorenz system, which is parameterized by shear stresses, shear strain and lubricant film temperature. The spatial inhomogeneity has been considered and it has been shown that a domain structure with two types of domains is formed during the friction process of contact surfaces planes through lubricant. The time dependencies of fractal dimensions of the domain distributions on a plane have been calculated and it has been shown that there is a time point, when fractal dimensions take the minimum values. It has been found, that the system tends to the homogeneous state, in which the same value of the shear stresses specifying the relative rate of the rubbing surfaces, is realized all over the contact plane.