Abstract
The features of dissipative structure formation, which is described by the periodic boundary value problem for the Kuramoto–Sivashinsky equation, are investigated. A numerical algorithm based on the pseudospectral method is presented. The efficiency and accuracy of the proposed numerical method are proved using the exact solution of the equation under study. Using the proposed method, the process of dissipative structure formation, which is described by the Kuramoto–Sivashinsky equation, is studied. The quantitative and qualitative characteristics of this process are described. It is shown that there is a value of the control parameter for which the dissipative structure formation processes occur. Via cyclic convolution, the average value of the control parameter is found. In addition, the dependence of the amplitude of the formed structures on the value of the control parameter is analyzed.
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Original Russian Text © N.A. Kudryashov, P.N. Ryabov, B.A. Petrov, 2015, published in Modelirovanie i Analiz Informatsionnykh Sistem, 2015, No. 1, pp. 105–113.
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Kudryashov, N.A., Ryabov, P.N. & Petrov, B.A. Dissipative structures of the Kuramoto–Sivashinsky equation. Aut. Control Comp. Sci. 49, 508–513 (2015). https://doi.org/10.3103/S0146411615070147
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DOI: https://doi.org/10.3103/S0146411615070147