Abstract
Problems of pseudoinversion of nonlinear differential models of spatially distributed dynamic systems are solved. Systems whose nonlinearity is formed by the product of linear differential transformations of the function of system’s state or by replacing the coefficients of linear approximation by these transformations are considered. Analytic dependences of the function of system’s state on continuously defined values of external-dynamic factors are constructed.
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V. A. Stoyan, “Creating integral mathematical models of two classes of nonlinear spatially distributed systems. I. The case of continuously defined external-dynamic perturbations,” Cybern. Syst. Analysis, Vol. 55, No. 5, 805–816 (2019).
N. F. Kirichenko and V. A. Stoyan, “Analytical representations of matrix and integral linear transformations,” Cybern. Syst. Analysis, Vol. 34, No. 3, 395–408 (1998).
V. A. Stoyan, “Methods of linear algebra in the analysis of certain classes of nonlinear discretely transformative systems. I . Multiplicative nonlinear systems,” Cybern. Syst. Analysis, Vol. 55, No. 1, 109–116 (2019).
V. A. Stoyan, “Methods of linear algebra in the analysis of certain classes of nonlinear discretely transformative systems. II. Systems with additively selected nonlinearity,” Cybern. Syst. Analysis, Vol. 55, No. 2, 259–264 (2019).
V. A. Stoyan and V.B. Dvirnychuk, “Constructing an integral equivalent of linear differential models,” Dopov. Nac. Akad. Nauk Ukr., No. 9, 36–43 (2012).
V. V. Skopetsky, V. A. Stoyan, and Iu. G. Kryvonos, Mathematical Modeling of Direct and Inverse Problems of the Dynamics of Distributed Parameter Systems [in Ukrainian], Naukova Dumka, Kyiv (2002).
V. A. Stoyan, Mathematical Modeling of Linear, Quasilinear, and Nonlinear Dynamic Systems [in Ukrainian], VPTs Kyivs’kyi Universytet, Kyiv (2011).
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Translated from Kibernetika i Sistemnyi Analiz, No. 1, January–February, 2020, pp. 118–128.
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Stoyan, V.A. Constructing Integral Mathematical Models of Two Classes of Nonlinear Spatially Distributed Systems. II. the Case of Continuously Defined External-Dynamic Perturbations*. Cybern Syst Anal 56, 100–109 (2020). https://doi.org/10.1007/s10559-020-00225-w
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DOI: https://doi.org/10.1007/s10559-020-00225-w