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A new approach for the computation of Hopf bifurcation points

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Abstract

A new approach is proposed to compute Hopf bifurcation points. The method could produce small extended systems and therefore could reduce the computational effort and storage. One numerical example is presented to demonstrate that the method is efficient.

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References

  1. Guchenheimer J, Holmes P.Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields[M]. New York: Springer-Verlag, 1983.

    Google Scholar 

  2. Roose D, De Dier B. Numerical determination of an emanating branch of Hopf bifurcation points in a two-parameter problem[J].SIAM J Sci Stat Comput, 1989,10(4):671–685.

    Article  MATH  Google Scholar 

  3. Roose D, Hlavacek V. A direct method for the computation of Hopf bifurcation points[J].SIAM J Appl Math, 1985,45(6):879–894.

    Article  MATH  MathSciNet  Google Scholar 

  4. Spence A, Cliffe K A, Jepson A D. A note on the calculation of paths of Hopf bifurcations[J].J Comput Appl Math, 1989,26(1):125–131.

    Article  MATH  MathSciNet  Google Scholar 

  5. Janovsky V, Plehac P. Asymptotic analysis of perturbed Hopf points[J].J Comput Appl Math, 1991,36(2):349–359.

    Article  MATH  MathSciNet  Google Scholar 

  6. Griewank A, Reddien G W. Characterization and computation of generalized turning points[J].SIAM J Numer Anal, 1989,21(1):186–196.

    MathSciNet  Google Scholar 

  7. Rapier P J, Reddien G W. Characterization and computation of singular points with maximum rank deficiency[J].SIAM J Numer Anal, 1986,23(5):1040–1051.

    Article  MathSciNet  Google Scholar 

  8. Keller H B. Numerical solution of bifurcation and nonlinear eigenvalue problems[A]. In: P H Rabinowitz, Ed.Applications of Bifurcation Theory[C]. New York: Academic Press, 1977,359–384.

    Google Scholar 

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Communicated by LIU Zeng-rong

Foundation item: the Natural Science Foundation of Guangdong Province (974006)

Biography: YE Rui-song (1968-)

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Rui-song, Y. A new approach for the computation of Hopf bifurcation points. Appl Math Mech 21, 1300–1307 (2000). https://doi.org/10.1007/BF02459252

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  • DOI: https://doi.org/10.1007/BF02459252

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