Skip to main content
SpringerLink
Log in

Dynamical behaviors of the brusselator system with impulsive input

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

Responses of dynamic system to pulse perturbations were investigated theoretically and experimentally. The model used in this paper has been proved dissipative by impulsive and dynamic theory. Complex phenomena such as limit cycles, periodic solutions, and chaos were numerically demonstrated.

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

Similar content being viewed by others

References

  1. Eiswirth M., Freund A., Ross J. (1991). Operational procedure toward the classification of chemical oscillators. J. Phys. Chem. 95, 1294–1299

    Article  CAS  Google Scholar 

  2. P. Gray, S.K. Scott, Chemical Oscillations and Instabilities: Non-linear Chemical Kinetics (Clarendon Press, 1994)

  3. P. Ilya, Time, structure and fluctuations. Noble Lecture 8, December (1977)

  4. J.J. Tyson, The Belousov-Zhabotinskii Reaction, vol. 10. (Springer-Verlag, Berlin, 1976)

  5. Tyson J.J., Liht J. (1973). Some further studies of nonlinear oscillations in chemical systems. J. Chem. Phys. 58, 3919–3930

    Article  CAS  Google Scholar 

  6. Selkoc E.E., Zhabotinskii A.M. (1967). Oscillatory Processes in Biological and Chemical Systems. Science Pub, Moscow

    Google Scholar 

  7. Zaikin A.N., Zhabotinskii A.M. (1970). Concentration wave propagation in two-dimensional liquid-phase. Nature 225, 535

    Article  CAS  Google Scholar 

  8. Bayliss A., Matkowsky B.J. (1994). From traveling to chaos in combustion. SIAM J. Appl. Math. 54(1): 1470–1474

    Article  Google Scholar 

  9. Bayliss A., Matkowsky B.J. (1990). Two routes to chaos in condensed phase combustion. SIAM J. Appl. Math. 50(2): 437–459

    Article  Google Scholar 

  10. Nicolis G., Prigogine I. (1977). Self-organization in Nonequilibrium Systems. Wiley, New York

    Google Scholar 

  11. Prigogine I., Lefever R. (1968). Symmetry breaking instabilities in dissipive systems—II. J. Chem. Phys. 48: 1659–1700

    Article  Google Scholar 

  12. C. Lansun, C. Jian, Nonlinear Biodynamical Systems (Science Publisher, 1993, In Chinese)

  13. Pomeau Y., Manneville P. (1980). Intermittent transition to turbulence in dissipative dynamical systems. Commun. Math. Phys. 74, 189–197

    Article  Google Scholar 

  14. Turing A.M. (1952). The chemical basis of morphogenesis. Phil. Trans. Roy. Soc. Lond. B237, 37

    Article  Google Scholar 

  15. Stoleriu I., Davidson F.A., Liu J.L. (2005). Effects of periodic input on the quasi-steady state assumptions for enzyme-catalysed reactions, J. Math. Biol. 50, 115–132

    Article  CAS  Google Scholar 

  16. Turner J.S. (1981). Alternating periodic and chaotic regimes in a chemical reaction experiment and theory. Phys. Lett. A 85, 9–12

    Article  Google Scholar 

  17. Stoleriu I., Davidson F.A., Liu J.L. (2004). Quasi-steady state assumptions for non-isolated enzyme-catalysed reactions, J. Math. Biol 48, 82–104

    Article  CAS  Google Scholar 

  18. D.D. Bainov, P.S. Simeonov (1993). Impulsive Differential Equations: Periodic Solutions and Applications. Longman Scientific and Technical, New York

    Google Scholar 

  19. Lakshmikantham V., Bainov D.D., Simeonov P.S. (1989). Theory of Impulsive Differential Equations. World Scientific, Singapore

    Google Scholar 

  20. Kubicek M., Hlavacek V. (1973). General parameter mapping technique: a procedure for solution of non-linear boundary value problems depending on an actual parameter. J. Inst. Math. Appl. 12, 287–293

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, P.R. China

    Mingjing Sun, Yuanshun Tan & Lansun Chen

  2. Department of Mathematics and Physics, Chongqing Jiaotong University, Chongqing, 400074, P.R. China

    Yuanshun Tan

Authors
  1. Mingjing Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuanshun Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lansun Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Mingjing Sun or Lansun Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sun, M., Tan, Y. & Chen, L. Dynamical behaviors of the brusselator system with impulsive input. J Math Chem 44, 637–649 (2008). https://doi.org/10.1007/s10910-008-9362-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-008-9362-y

Keywords

Search

Navigation