Practical bifurcation and stability analysis. 3rd ed.

*(English)*Zbl 1195.34004
Interdisciplinary Applied Mathematics 5. New York, NY: Springer-Verlag (ISBN 978-1-4419-1739-3/hbk; 978-1-4614-2530-4/pbk; 978-1-4419-1740-9/ebook). xviii, 483 p. (2010).

Methods of practical bifurcation and stability analysis are crucial instruments in applied mathematics. This fact stimulated the author to publish an up-to-date third edition, sixteen years after the second edition. In order to include recent developments, the entire book has been thoroughly revised. Essential changes concern the third chapter of the second edition which has been replaced by the new Chapter 3 which contains expositions on waves, pattern formation and existable media, but also contributions to delay differential equations, nonsmooth dynamics and differential algebraic equations. Several sections have been expanded, new sections (e.g. chaos control) have been included. The references contain more than 600 items. The excellent presentation of the material will stimulate people in applied sciences to apply the well-prepared instruments.

The first edition has been reviewed in [From equilibrium to chaos. Practical bifurcation and stability analysis. New York etc.: Elsevier (1988; Zbl 0652.34059)].

The first edition has been reviewed in [From equilibrium to chaos. Practical bifurcation and stability analysis. New York etc.: Elsevier (1988; Zbl 0652.34059)].

Reviewer: Klaus R. Schneider (Berlin)

##### MSC:

34-02 | Research exposition (monographs, survey articles) pertaining to ordinary differential equations |

34Cxx | Qualitative theory for ordinary differential equations |

34Dxx | Stability theory for ordinary differential equations |

65P30 | Numerical bifurcation problems |

70Kxx | Nonlinear dynamics in mechanics |

92-08 | Computational methods for problems pertaining to biology |

65L07 | Numerical investigation of stability of solutions |

37Mxx | Approximation methods and numerical treatment of dynamical systems |

37Nxx | Applications of dynamical systems |