## Bifurcation Theory & Its Numerical AnalysisBifurcation theory consists of two distinct aspects - static and dynamic. Static bifurcation theory deals with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied, while the dynamic one is concerned with the changes that occur in the structure of the limit sets of solutions of differential equations as parameters in the vector field are varied. Its extensive research and numerical analyses have been conducted in the past years. This book contains eighteen refereed papers presented at the conference, held in Xi'an, China, June 29 - July 3, 1998. The papers cover recent development of a wide range of theoretical and numerical issues of bifurcation theory. They also involve its applications to such important areas as fluid flows, elasticity, elastic-plastic solids, neuron transport, robotics, activator-inhibitor modeling, and biology. |

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### Contents

Preface | 1 |

Some Problems in Mathematical Modeling and Simulation | 28 |

Numerical Experiments for a Finite Element Approximation | 41 |

Copyright | |

12 other sections not shown

### Common terms and phrases

1999 by Springer Anal analysis approximation assume assumption asymptotically Banach space bifurcation diagrams bifurcation point bifurcation solution Bifurcation Theory Bogdanov-Takens bifurcation boundary BTNA'98 Proceedings Chen Chow codimension compact computation cones consider convergence convex coordinates Copyright 1999 defined denote differential equations dimensional DS point eigenvalue problems elliptic error estimates exists Figure finite element method fixed point fixed-point subspace flow form reserved function given global Hence heteroclinic cycles homoclinic orbits Hopf bifurcation Hopf points initial conditions invariant foliations isotropy Lemma linear Math Mathematics matrix mixed finite element mode interaction neighborhood neutron nonlinear normal form numerical orbit overflowing manifold parameters periodic solutions perturbation pitchfork bifurcation porous medium positive solutions Proof prove pseudo-orbit pseudo-orbit shadowing property result rights of reproduction satisfying semiflow sensitive dependence SIAM singular solve Springer All rights stability standing wave steady-state subspace symmetry Theorem 2.1 unique unstable manifold variable velocity zero