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Parameter Identification in a Respiratory Control System Model with Delay

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Mathematical Modeling and Validation in Physiology

Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 2064))

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Abstract

In this paper we study parameter identification issues by computational means for a set of nonlinear delay equations which have been proposed to model the dynamics of a simplified version of the respiratory control system. We design specific inputs for our system to produce “information rich” output data needed to determine values of unknown parameters. We also consider the effects of noisy measurements in the identification process. Several case studies are included.

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References

  1. Banks, H.T., Burns, J.A., Cliff, E.M.: Parameter estimation and identification for systems with delays. SIAM J. Contr. Optim. 19(6), 791–828 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  2. Banks, H.T., Daniel Lamm, P.K.: Estimation of delays and other parameters in nonlinear functional differential equations. SIAM J. Contr. Optim. 21(6), 895–915 (1983)

    Google Scholar 

  3. Batzel, J.J., Tran, H.T.: Stability of the human respiratory control system: I. Analysis of a two-dimensional delay state-space model. J. Math. Biol. 41, 45–79 (2000)

    MathSciNet  MATH  Google Scholar 

  4. Batzel, J.J., Tran, H.T.: Stability of the human respiratory control system: II. Analysis of a three-dimensional delay state-space model. J. Math. Biol. 41, 80–102 (2000)

    MathSciNet  MATH  Google Scholar 

  5. Cooke, K.L., Turi, J.: Stability, instability in delay equations modeling human respiration. J. Math. Biol. 32, 535–543 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cooke, K.L., Wiener, J.: Retarded differential equations with piecewise constant delays. J. Math. Anal. Appl. 99, 265–297 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cooke, K.L., Wiener, J.: Stability regions for linear equations with piecewise continuous delays. Comput. Math. Appl. 12A, 695–701 (1986)

    Article  MathSciNet  Google Scholar 

  8. Cooke, K.L., Wiener, J.: A survey of differential equations with piecewise continuous arguments. In: Busenberg, S., Martelli, M. (eds.) Delay Differential Equations and Dynamical Systems. Lecture Notes in Mathematics, vol. 1475, pp. 1–15. Springer, Berlin (1991)

    Chapter  Google Scholar 

  9. Dennis, J.E., Schnabel, R.B.: Numerical methods for unconstrained optimization and nonlinear equations. Prentice-Hall, Englewood Cliffs, NJ (1983)

    MATH  Google Scholar 

  10. Győri, I.: On approximation of the solutions of delay differential equations by using piecewise constant arguments. Int. J. Math. Math. Sci. 14(1), 111–126 (1991)

    Article  Google Scholar 

  11. Győri, I., Hartung, F., Turi, J.: Numerical approximations for a class of differential equations with time- and state-dependent delays. Appl. Math. Lett. 8(6), 19–24 (1995)

    Article  MathSciNet  Google Scholar 

  12. Hartung, F., Herdman, T.L., Turi, J.: On existence, uniqueness and numerical approximation for neutral equations with state-dependent delays. Appl. Numer. Math. 24, 393–409 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hartung, F., Herdman, T.L., Turi, J.: Parameter identification in classes of hereditary systems of neutral type. Appl. Math. Comput. 89(1-3), 147–160 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hartung, F., Herdman, T.L., Turi, J.: Parameter identifications in classes of neutral differential equations with state-dependent delays. Nonlinear Anal. 39(3), 305–325 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. Hartung, F., Krisztin, T., Walther, H.O., Wu, J.: Functional differential equations with state-dependent delays: Theory and applications. In: Canada, A., Drabek, P., Fonda, A. (eds.) Handbook of Differential Equations, vol. 3, pp. 435–545. Elsevier, Amsterdam (2006)

    Google Scholar 

  16. Hartung, F., Turi, J.: Identification of parameters in delay equations with state-dependent delays. Nonlinear Anal. 29(11), 1303–1318 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hartung, F., Turi, J.: Linearized stability in functional differential equations with state-dependent delays. Discrete and Continuous Dynamical Systems (Added Volume), 416–425 (2001). Dynamical Systems and Delay Differential Equations (Kennesaw, GA, 2000)

    Google Scholar 

  18. Lunel, S.M.V.: Parameter identifiability of differential delay equations. Int. J. Adapt. Contr. Signal Process. 15, 655–678 (2001)

    Article  MATH  Google Scholar 

  19. Nakagiri, S., Yamamoto, M.: Identifiability of linear retarded systems in Banach spaces. Funkcial. Ekvac. 31, 315–329 (1988)

    MathSciNet  MATH  Google Scholar 

  20. Wiener, J.: Generalized Solutions of Functional Differential Equations. World Scientific, Singapore (1993)

    MATH  Google Scholar 

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Acknowledgements

This research was partially supported by the National Science Foundation under grant DMS-0705247 (FH and JT) and by Hungarian NFSR Grant No. K101217 (FH).

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Authors and Affiliations

  1. Department of Mathematics, University of Pannonia, Veszprém, H-8201, Hungary

    Ferenc Hartung

  2. Programs in Mathematical Sciences, University of Texas at Dallas, Richardson, TX, 75083, USA

    Janos Turi

Authors
  1. Ferenc Hartung
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  2. Janos Turi
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Corresponding author

Correspondence to Janos Turi .

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Editors and Affiliations

  1. Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, Graz, 8010, Austria

    Jerry J. Batzel

  2. College of Sciences, Department of Mathematics, King Saud University, King Khalid Road, Diriyah Campus, Riyadh, 11451, Saudi Arabia

    Mostafa Bachar

  3. Institute for Mathematics, and Scientific Computing, University of Graz, Heinrichstrasse 36, Graz, 8010, Austria

    Franz Kappel

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Hartung, F., Turi, J. (2013). Parameter Identification in a Respiratory Control System Model with Delay. In: Batzel, J., Bachar, M., Kappel, F. (eds) Mathematical Modeling and Validation in Physiology. Lecture Notes in Mathematics(), vol 2064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32882-4_6

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