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Local and Global Bifurcations

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Abstract

This chapter introduces some local and global bifurcation theory in the plane.

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Bibliography

  1. T. Becker, V. Weispfenning and H. Kredel, Gröbner Bases: A Computational Approach to Commutative Algebra (Graduate Texts in Mathematics), Springer, New York, 2012.

    Google Scholar 

  2. T.R. Blows and L.M. Perko, Bifurcation of limit cycles from centers and separatrix cycles of planar analytic systems, SIAM Review, 36 (1994), 341–376.

    Google Scholar 

  3. H. Broer, I. Hoveijn, G, Lunter, G. Vegter, Bifurcations in Hamiltonian Systems: Computing Singularities by Gröbner Bases (Lecture Notes in Mathematics), Springer-Verlag, New York, 2003.

    Google Scholar 

  4. B. Buchberger Ed., Gröbner Bases and Applications (London Mathematical Society Lecture Note Series), Cambridge University Press, Cambridge, UK, 1998.

    Google Scholar 

  5. B. Buchberger, On Finding a Vector Space Basis of the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal, PhD thesis, University of Innsbruck, Austria, 1965 (German).

    Google Scholar 

  6. T. Hibi (Editor), Gröbner Bases: Statistics and Software Systems, Springer, New York, 2013.

    Google Scholar 

  7. N. Lauritzen, Concrete Abstract Algebra: From Numbers to Gröbner Bases, Cambridge University Press, Cambridge, UK, 2003.

    Google Scholar 

  8. N.G. Lloyd, Limit cycles of polynomial systems, New Directions in Dynamical Systems (ed. T. Bedford and J. Swift), L.M.S. Lecture Notes Series No. 127, Cambridge University Press, Cambridge, UK, 1988.

    Google Scholar 

  9. N.G. Lloyd and S. Lynch, Small-amplitude limit cycles of certain Liénard systems, Proc. Roy. Soc. Lond. Ser. A, 418 (1988), 199–208.

    Google Scholar 

  10. S. Lynch, Symbolic computation of Lyapunov quantities and the second part of Hilbert’s sixteenth problem, in Differential Equations with Symbolic Computation, D.M. Wang and Z. Zheng Eds., Birkhäuser, Basel, Cambridge, MA, 2005.

    Google Scholar 

  11. H. Maoan and Y. Pei, Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles (Applied Mathematical Sciences, Vol. 181), Springer, New York, 2012

    Google Scholar 

  12. D.M. Wang, Elimination Practice: Software Tools and Applications, Imperial College Press, London, 2004.

    Google Scholar 

  13. D.M. Wang, Polynomial systems from certain differential equations, J. Symbolic Computation, 28 (1999), 303–315.

    Google Scholar 

  14. I. Yengui, Constructive Commutative Algebra: Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases (Lecture Notes in Mathematics), Springer, New York, 2015.

    Google Scholar 

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Correspondence to Stephen Lynch .

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Lynch, S. (2017). Local and Global Bifurcations. In: Dynamical Systems with Applications Using Mathematica®. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-61485-4_10

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