Skip to main content
SpringerLink
Log in

Computation of Optimal Disturbances for Delay Systems

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

Novel fast algorithms for computing the maximum amplification of the norm of solution and optimal disturbances for delay systems are proposed and justified. The proposed algorithms are tested on a system of four nonlinear delay differential equations providing a model for the experimental infection caused by the lymphocytic choriomeningitis virus (LCMV). Numerical results are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.

Similar content being viewed by others

REFERENCES

  1. A. V. Boiko, Yu. M. Nechepurenko, and M. Sadkane, “Fast computation of optimal disturbances for duct flows with a given accuracy,” Comput. Math. Math. Phys. 50, 1914–1924 (2010).

    Article  MathSciNet  Google Scholar 

  2. A. V. Boiko, Y. M. Nechepurenko, and M. Sadkane, “Computing the maximum amplification of the solution norm of differential-algebraic systems,” Comput. Math. Model. 23 (2), 216–227 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  3. Y. M. Nechepurenko and M. Sadkane, “A low-rank approximation for computing the matrix exponential norm,” SIAM J. Matrix. Anal. Appl. 32 (2), 349–363 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  4. G. A. Bocharov, Yu. M. Nechepurenko, M. Yu. Khristichenko, and D. S. Grebennikov, “Optimal disturbances of delay system for controlling the dynamics of infectious diseases based on multicomponent actions,” Modern. Math. Fundam. Drections 63 (3), 392–417 (2017).

    Google Scholar 

  5. G. A. Bocharov, Yu. M. Nechepurenko, M. Yu. Khristichenko, and D. S. Grebennikov, Control of models of virus infections with delayed variables, based on optimal disturbances, Preprint no. 52, IPM RAN (Keldysh Ins. of Applied Mathematics, Russian Academy of Sciences, 2017).

  6. G. A. Bocharov, Yu. M. Nechepurenko, M. Yu. Khristichenko, and D. S. Grebennikov, “Maximum response perturbation-based control of virus infection model with time-delays,” Russ. J. Num. Anal. Math. Model. 32 (5), 275–291 (2017).

    MathSciNet  MATH  Google Scholar 

  7. G. A. Bocharov, Yu. M. Nechepurenko, M. Yu. Khristichenko, and D. S. Grebennikov, “Optimal disturbances of bistable time-delay systems modeling virus infections,” Dokl. Math. 98, 313–316 (2018).

    Article  MATH  Google Scholar 

  8. G. A. Bocharov, “Modelling the dynamics of LCMV infection in mice: Conventional and exhaustive CTL responses,” J. Theor. Biol. 192 (3), 283–308 (1998).

    Article  Google Scholar 

  9. Y. M. Nechepurenko and M. Sadkane, “Computing humps of the matrix exponential,” J. Comput. Appl. Math. 319, 87–96 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  10. E. Hairer, S. Nørsett, and G. Wanner, Solving Ordinary Differential Equations (Springer, Berlin, 1987).

    Book  MATH  Google Scholar 

  11. G. H. Golub and C. F. van Loan, Matrix Computations ((John Hopkins Univ. Press, London, 1989).

    MATH  Google Scholar 

  12. B. N. Parlett, The Symmetric Eigenvalue Problem (SIAM, Berkeley, 1998).

    Book  MATH  Google Scholar 

Download references

Funding

The algorithms were substantiated with the financial support of the program of the Presidium of the Russian Academy of Sciences no. 01 “Fundamental Mathematics and Its Applications,” project no. PRAS-18-01.

The development and implementation of the algorithms was supported by the Russian Science Foundation, project no. 17-71-21049.

Author information

Authors and Affiliations

  1. Marchuk Institute of Computational Mathematics, Russian Academy of Sciences, 119333, Moscow, Russia

    Yu. M. Nechepurenko

  2. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia

    M. Yu. Khristichenko

Authors
  1. Yu. M. Nechepurenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Yu. Khristichenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Yu. Khristichenko.

Additional information

Translated by A. Klimontovich

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nechepurenko, Y.M., Khristichenko, M.Y. Computation of Optimal Disturbances for Delay Systems. Comput. Math. and Math. Phys. 59, 731–746 (2019). https://doi.org/10.1134/S0965542519050129

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542519050129

Keywords:

Search

Navigation