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On One Class of Systems of Differential Equations and on Retarded Equations

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Abstract

We establish a connection between solutions to a broad class of large systems of ordinary differential equations and solutions to retarded differential equations. We prove that solving the Cauchy problem for systems of ordinary differential equations reduces to solving the initial value problem for a retarded differential equation as the number of equations increases unboundedly. In particular, the class of systems under consideration contains a system of differential equations which arises in modeling of multiphase synthesis.

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References

  1. Likhoshvai V. A., Fadeev S. I., Demidenko G. V., and Matushkin Yu. G., “Modeling by a delay equation of multiphase synthesis without bifurcation,” Sibirsk. Zh. Industr. Mat., 7, No.1, 73–94 (2004).

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  2. Demidenko G. V., Kolchanov N. A., Likhoshvai V. A., Matushkin Yu. G., and Fadeev S. I., “Mathematical modeling of regulator contours of gene nets,” Zh. Vychisl. Mat. i Mat. Fiziki, 44, No.12, 2276–2295 (2004).

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  3. Demidenko G. V. and Likhoshvai V. A., “On differential equations with retarded argument,” Siberian Math. J., 46, No.3, 417–430 (2005).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    G. V. Demidenko

  2. Institute of Cytology and Genetics, Novosibirsk, Russia

    V. A. Likhoshvai

  3. Novosibirsk State University, Novosibirsk, Russia

    T. V. Kotova & Yu. E. Khropova

Authors
  1. G. V. Demidenko
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  2. V. A. Likhoshvai
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  3. T. V. Kotova
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  4. Yu. E. Khropova
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Additional information

The authors were supported by the Russian Foundation for Basic Research (Grants 04-01-00458, 05-07-98011, 05-07-98012, and 05-04-08084), the Program of the Federal Agency for Education (Grant 8273), and NSF:FIBR (Grant EF-0330786).

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 58–68, January–February, 2006.

Original Russian Text Copyright © 2006 Demidenko G. V., Likhoshvai V. A., Kotova T. V., and Khropova Yu. E.

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Demidenko, G.V., Likhoshvai, V.A., Kotova, T.V. et al. On One Class of Systems of Differential Equations and on Retarded Equations. Sib Math J 47, 45–54 (2006). https://doi.org/10.1007/s11202-006-0005-x

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  • DOI: https://doi.org/10.1007/s11202-006-0005-x

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