V.O. Afenchenko1, S.V. Kiyashko2, V.V. Chernov3

1-3 Institute of Applied Physics of Russian Academy of Science (Nizhny Novgorod, Russia)

1 afen@appl.sci-nnov.ru; 2 kiyashko@appl.sci-nnov.ru; 3 vcher@ipfran.ru

In nonlinear systems with instability, multistability often occurs. When studying processes occurring in real environments, the problem arises of finding paths leading to any state of equilibrium and searching for new stable states. In two-dimensional systems, they can consist of domains and differ in orientation in space.

The goal of the work is to experimentally determine the features of the generation of multidomain structures in a two-dimensional system in the presence of complex boundaries of a liquid layer that experiences periodic vertical oscillations.

The paper presents the results of an experimental study of the dynamics of roller domains of parametrically excited capillary waves in a square cell with a square insert in the center of the cell. In different domains, the rollers were oriented parallel and perpendicular to the boundaries of the cuvette and the boundaries of the square insert. It was found that the dynamics of domains is determined by the movement of their fronts, and depending on the initial and boundary conditions, stable two-dimensional roller structures can appear at the edges of the cuvette with a rounded corner and a rectangular protrusion. In different domains, the rollers had different orientations. In this case, roundings with a large radius had the strongest effect on the dynamics of defects.

Multistability of equilibrium states of roller structures was discovered, characterized by the fact that, with constant system parameters, different scenarios of domain competition arose, leading to 7 different stable equilibrium states, which differed in the number of domains, their shape and the presence of spatial symmetry. It has been experimentally shown that the most stable equilibrium states of domains arise when the square protrusion is symmetrically positioned relative to the sides of the cuvette. It has been established that by creating additional initial disturbances at the cell boundary, it is possible to control the multistability of stable equilibrium states of competing domains.

The results obtained may be of interest when studying the processes of establishing stable regimes in active media under strong competition and when studying the formation of two-dimensional structures from conducting particles capable of scattering electromagnetic waves.

Afenchenko V.O., Kiyashko S.V., Chernov V.V. Control of multistability of roller structures under parametric excitation of capillary waves in a square cell with internal boundaries. Nonlinear World. 2023. V. 21. № 4. P. 24-32. DOI: https://doi.org/10.18127/j20700970-202304-03 (In Russian)

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