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Mathematical Modeling of Quadratically Nonlinear Spatially Distributed Systems. I. The Case of Discretely Defined Initial–Boundary External-Dynamic Perturbations

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Abstract

Two classes of nonlinear spatially distributed dynamical systems discretely observed according to the initial–boundary and spatially distributed external-dynamic disturbances 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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Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    V. A. Stoyan

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  1. V. A. Stoyan
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Correspondence to V. A. Stoyan.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 5, September–October, 2021, pp. 84–97.

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Stoyan, V.A. Mathematical Modeling of Quadratically Nonlinear Spatially Distributed Systems. I. The Case of Discretely Defined Initial–Boundary External-Dynamic Perturbations. Cybern Syst Anal 57, 740–753 (2021). https://doi.org/10.1007/s10559-021-00399-x

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