Abstract
This chapter introduces some local and global bifurcation theory in the plane.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
T. Becker, V. Weispfenning and H. Kredel, Gröbner Bases: A Computational Approach to Commutative Algebra (Graduate Texts in Mathematics), Springer, New York, 2012.
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.
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.
B. Buchberger Ed., Gröbner Bases and Applications (London Mathematical Society Lecture Note Series), Cambridge University Press, Cambridge, UK, 1998.
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).
T. Hibi (Editor), Gröbner Bases: Statistics and Software Systems, Springer, New York, 2013.
N. Lauritzen, Concrete Abstract Algebra: From Numbers to Gröbner Bases, Cambridge University Press, Cambridge, UK, 2003.
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.
N.G. Lloyd and S. Lynch, Small-amplitude limit cycles of certain Liénard systems, Proc. Roy. Soc. Lond. Ser. A, 418 (1988), 199–208.
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.
H. Maoan and Y. Pei, Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles (Applied Mathematical Sciences, Vol. 181), Springer, New York, 2012
D.M. Wang, Elimination Practice: Software Tools and Applications, Imperial College Press, London, 2004.
D.M. Wang, Polynomial systems from certain differential equations, J. Symbolic Computation, 28 (1999), 303–315.
I. Yengui, Constructive Commutative Algebra: Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases (Lecture Notes in Mathematics), Springer, New York, 2015.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-61485-4_10
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-61484-7
Online ISBN: 978-3-319-61485-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)