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On The Stability Of Some Non-Stationary Nonlinear Systems, Rustamjon V. Mullajonov, Shakhodathon N. Abdugapparova, Jumagul V. Mirzaahmedova

Scientific Bulletin. Physical and Mathematical Research

The objective of the theory of stability of motion is to establish signs that make it possible to judge whether the motion in question is stable or unstable. Since in reality perturbing factors always inevitably exist, it becomes clear that the problem of stability of movement assumes very important theoretical and practical significance.

Mathematical modeling of processes and phenomena in animate and inanimate nature always involves a certain classification of them in accordance with their complexity. Many processes and phenomena are modeled by large-scale systems (CMS), which consist of separate subsystems, united by communication functions. In many cases, CMS is …

Synergetic Simulation Of Nanostructure Growth Processes In The Volume Of Mesophase Of Silicon And Germanium, Sirojiddin Z. Zainabidinov, Bakhodirjon Askarov, Shukhratjon K. Akbarov

Scientific Bulletin. Physical and Mathematical Research

A new approach is proposed for studying the processes of nanoparticle growth under nonequilibrium conditions associated with vibronic effects. The adiabatic potential for studying atomic rearrangements of a local group of atoms is constructed. The nanoparticle growth process was studied by the method of synergetic modeling, taking into account the anharmonic terms in the adiabatic potential. Based on the methods of catastrophe theory, the conditions for the instability in a local group of atoms are found. It is shown that the number of bound atoms in a local group affects the stability of the local group of atoms. An analytical …