Abstract
Two classes of nonlinear spatially distributed dynamical systems discretely observed according to the initial–boundary and spatially distributed external-dynamic perturbations are analyzed. For each of them, analytical dependences are constructed for the state function, which agrees, according to the root-mean square criterion, with the available information on external-dynamic conditions of their operation. Solution of the initial–boundary-value problems for the systems under study is defined in terms of a set of vectors, which, according to the root-mean-square criterion, model the given initial–boundary environment, including the spatially distributed external-dynamic perturbations. Conditions of the accuracy and uniqueness of the obtained mathematical results are presented. The cases of unbounded spatial domains and systems’ steady-state dynamics are considered.
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Continued from Cybernetics and Systems Analysis, Vol. 57, No. 5, 2021.
Translated from Kibernetyka ta Systemnyi Analiz, No. 6, November–December, 2021, pp. 72–83.
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Stoyan, V.A. Mathematical Modeling of Quadratically Nonlinear Spatially Distributed Systems. II. The Case of Continuously Defined Initial–Boundary External-Dynamic Perturbations. Cybern Syst Anal 57, 906–917 (2021). https://doi.org/10.1007/s10559-021-00417-y
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DOI: https://doi.org/10.1007/s10559-021-00417-y