Skip to main content

Stochastic Hybrid Delay Population Dynamics

  • Conference paper
Hybrid Systems: Computation and Control (HSCC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3927))

Included in the following conference series:

Abstract

In this paper we will investigate a stochastic hybrid delay population dynamics (SHDPD) and show under certain conditions, the SHDPD will have global positive solution. Ultimate boundedness and extinction, two important properties in a population systems, are discussed.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahmad, A., Rao, M.R.M.: Asymptotically periodic solutions of n-competing species problem with time delay. J. Math. Anal. Appl. 186, 557–571 (1994)

    Article  MathSciNet  Google Scholar 

  2. Athans, M.: Command and control (c2) theory: A challenge to control science. IEEE Trans. Automat. Control 32, 286–293 (1987)

    Article  Google Scholar 

  3. Basak, G.K., Bisi, A., Ghosh, M.K.: Stability of a random diffusion with linear drift. J. Math. Anal. Appl. 202, 604–622 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bereketoglu, H., Gyori, I.: Global asymptotic stability in a nonautonomous Lotka-Volterra type system with infinite delay. J. Math. Anal. Appl. 210, 279–291 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bahar, A., Mao, X.: Stochastic delay Lotka-Volterra model. J. Math. Anal. Appl. 292, 364–380 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Freedman, H.I., Ruan, S.: Uniform persistence in functional differential equations. J. Differential Equations 115, 173–192 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gopalsamy, K.: Stability and Oscillations in Delay Differential Equations of Population Dynamics. Kluwer Academic, Dordrecht (1992)

    Book  MATH  Google Scholar 

  8. He, X., Gopalsamy, K.: Persistence, attractivity, and delay in facultative mutualism. J. Math. Anal. Appl. 215, 154–173 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hu, J., Wu, W., Sastry, S.: Modeling subtilin production in bacillus subtilis using stochastic hybrid systems. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 417–431. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  10. Kazangey, T., Sworder, D.D.: Effective federal policies for regulating residential housing. In: Proc. Summer Computer Simulation Conference, San diego, pp. 1120–1128 (1971)

    Google Scholar 

  11. Kolmanovskii, V., Myshkis, A.: Applied Theory of Functional Differential Equations. Kluwer Academic Publishers, Dordrecht (1992)

    Book  MATH  Google Scholar 

  12. Kuang, Y.: Delay Differential Equations with Applications in Population Dynamics. Academic Press, Boston (1993)

    MATH  Google Scholar 

  13. Kuang, Y., Smith, H.L.: Global stability for infinite delay Lotka-Volterra type systems. Differential Equations 103, 221–246 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  14. Liptser, R.S., Shiryayev, A.N.: Theory of Martingales. Kluwer Academic Publishers, Dordrecht (1989) (Translation of the Russian edition, Nauka, Moscow, 1986)

    Book  MATH  Google Scholar 

  15. Mariton, M.: Jump Linear Systems in Automatic Control, Marcel Dekker, New York (1990)

    Google Scholar 

  16. Skorohod, A.V.: Asymptotic Methods in the Theory of Stochastic Differential Equations. American Mathematical Society, Providence (1989)

    Google Scholar 

  17. Sworder, D.D., Rogers, R.O.: An LQ-solution to a control problem associated with a solar thermal central receiver. IEEE Trans. Automat. Control 28, 971–978 (1983)

    Article  Google Scholar 

  18. Teng, Z., Yu, Y.: Some new results of nonautomomous Lotka-Volterra competitive systems with delays. J. Math. Anal. Appl. 241, 254–275 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  19. Willsky, A.S., Levy, B.C.: Stochastic stability research for complex power systems, DOE Contract, LIDS, MIT, Rep. ET-76-C-01-2295 (1979)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lygeros, J., Mao, X., Yuan, C. (2006). Stochastic Hybrid Delay Population Dynamics. In: Hespanha, J.P., Tiwari, A. (eds) Hybrid Systems: Computation and Control. HSCC 2006. Lecture Notes in Computer Science, vol 3927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11730637_33

Download citation

  • DOI: https://doi.org/10.1007/11730637_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33170-4

  • Online ISBN: 978-3-540-33171-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics