2 edition of **Continuation techniques and bifurcation problems** found in the catalog.

Continuation techniques and bifurcation problems

- 381 Want to read
- 4 Currently reading

Published
**1990**
by Birkhäuser Verlag in Basel, Boston
.

Written in English

- Bifurcation theory.,
- Continuation methods.,
- Differential equations, Nonlinear -- Numerical solutions.

**Edition Notes**

Statement | edited by Hans D. Mittelmann, Dirk Roose. |

Series | International series of numerical mathematics =, Internationale Schriftenreihe zur numerischen Mathematik =, Série international d"analyse numérique ;, vol. 92, International series of numerical mathematics ;, v. 92. |

Contributions | Mittelmann, H. D., 1945-, Roose, Dirk. |

Classifications | |
---|---|

LC Classifications | QA372 .C643 1990 |

The Physical Object | |

Pagination | 218 p. : |

Number of Pages | 218 |

ID Numbers | |

Open Library | OL2225895M |

ISBN 10 | 0817623973 |

LC Control Number | 89070793 |

Mittelmann, H. D.; Roose, D., Continuation Techniques and Bifurcation Problems. Basel etc., Birkhäuser Verlag pp., sfr —. ISBN (ISNM 92)Author: Ch. Grossmann. Applications of numerical continuation techniques. Numerical continuation techniques have found a great degree of acceptance in the study of chaotic dynamical systems and various other systems which belong to the realm of catastrophe theory. The reason for such usage stems from the fact that various non-linear dynamical systems behave in a deterministic and predictable manner within a range of .

20 November | International Journal of Bifurcation and Chaos, Vol. 12, No. 08 An automatic continuation strategy for the solution of singularly perturbed nonlinear boundary value problems J. R. Cash, G. Moore and R. W. WrightCited by: techniques to a diverse set of ﬂuid mechanical problems. AMS subject classiﬁcations: 37H20,35Q35, ,37M, 65P30 Key words: Numerical bifurcation analysis, transitions in ﬂuid ﬂows, high-dimensional dynami-cal systems. Contents 1 Introduction 2 2 The methodologyof continuation 4 3 Computation of bifurcation diagrams 10 4 Highlights of File Size: 3MB.

Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay.5/5(1). for numerical bifurcation analysis. We adapt the continued subspace to track behavior relevant to bifurcations, and use projection methods to deal with large problems. To test our ideas, we have integrated our code into Matcont, a program for numerical continuation and bifurcation analysis. 1. Introduction. Parameter-dependent Jacobian matrices Cited by:

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Numerical continuation techniques allow the efficient computation of solution branches in a one-parameter problem. In many cases continuation procedures are used as part of a more complete analysis of a nonlinear problem, based on bifurcation theory and singularity : Fischer.

Numerical continuation techniques allow the efficient computation of solution branches in a one-parameter problem. In many cases continuation procedures are used as part of a more complete analysis of a nonlinear problem, based on bifurcation theory and singularity theory.

These theories contribute to the understanding of many nonlinear phenomena in nature and they form the basis for. The analysis of parameter-dependent nonlinear has received much attention in recent years.

Numerical continuation techniques allow the efficient computation of solution branches in a one-parameter problem. In many cases continuation procedures are used as. Continuation Techniques and Bifurcation Problems. Summary: In many cases continuation procedures are used as part of a more complete analysis of a nonlinear problem, based on bifurcation theory and singularity theory.

Additional Physical Format: Online version: Continuation techniques and bifurcation problems. Basel ; Boston: Birkhäuser Verlag, (OCoLC) Continuation and Bifurcations: Numerical Techniques and Applications.

Editors (view affiliations) A Newton-Like Method for Simple Continuation techniques and bifurcation problems book Problems with Application to Large Sparse Systems Pages LINLBF: A Program for Continuation and Bifurcation Analysis of Equilibria Up to Codimension Three. Khibnik. Pages On.

Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve.

The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis.

apply the techniques presented here. His software displays the continuation path, solutions, and much more. His normalization equation, N and branch switching algorithm is a bit more sophisticated. He also utilizes a user defined functional on B to help with graphing and continuation.

Solving with PLTMG The numerical analysis of bifurcation problems is concerned with the stable, reliable and eﬃcient computation of solutions to multiparameter nonlinear problems. We shall consider numerical methods for solving nonlinear equa-tions of the form F(x,λ) = 0, () where Fis a smooth operator in an appropriate Banach space setting, xisCited by: Lectures on Numerical Methods In Bifurcation Problems By H.B.

Keller Lectures delivered at the Indian Institute Of Science, Bangalore These lectures introduce the modern theory of continuation or path fol-lowing in scientiﬁc computing. Almost all problem in scienc e and tech- results obtained using some of the techniques presented in.

Continuation Techniques and Bifurcation Problems (International Series of Numerical Mathematics) (Reprint Edition) by Dirk (Ed.) Roose, Hans D.

Mittelmann, H.D. Mittelmann (Editor) Paperback, Pages, Published ISBN / ISBN / Need it Fast. 2 day shipping options The analysis of parameter-dependent Book Edition: Reprint Edition. The favorable reaction to the ﬁrst edition of this book conﬁrmed that the publication of such an application-oriented text on bifurcation theory of dynamical systems was well timed.

The selected topics indeed cover ma-jor practical issues of applying the bifurcation theory to ﬁnite-dimensional problems. Continuation techniques and interactive software for bifurcation analysis of ODEs and iterated maps Alexander I.

Khibnik 1, Yuri A. Kuznetsov 2, Victor V. Levitin and Eugene V. Nikolaev. But one should be careful in interpreting the results when (6) this difference becomes essential once more. Khibnik et al.

/ Continuation techniques and interactive software The phase part of the determining system is written as follows: for equilibrium points of (1) F(x, a)=0, (9) - for fixed points (p = 1) and periodic orbits (p > 1) of (2) Fx,a)-x=0, system has the form 0i(x, a) = 0, i/t(x, a) = 0, (14) Cited by: A key development in the eld was the introduction of bifurcation and continuation methods to problems in ight dynamics by Carroll and Mehra,15 and Zagaynov and Goman The use of continuation algorithms made it possible to smartly compute an entire family of steady state (trim) solutions for varying values of aFile Size: 1MB.

Continuation Techniques and Bifurcation Problems, () Large sparse continuation problems. Journal of Computational and Applied MathematicsCited by: the continuation and bifurcation analysis of DDEs that are implemented in the software packages DDE-Biftool [25, 26] and PDDE-Cont [73].

Where appropriate, we also brieﬂy describe alternative numerical methods. Note that we do not discuss time integration of DDEs; for this topic see, e.g., [2] and [6].

The structure of this chapter is as follows. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can book opens with a foreword by Herbert B.

Keller and lecture notes by Sebius. A Newton-Like Method for Simple Bifurcation Problems with Application to Large Sparse Systems. Continuation and Bifurcations: Numerical Techniques and Applications, () On the numerical solution of double-periodic elliptic eigenvalue by: The more general concept of a continuation strategy is also discussed.

It allows the analysis of various singularities of generic systems and of their mutual relationships. The approach is extended to codimension three singularities. We introduce several bifurcation functions and show how to use them to construct well-posed continuation by:.

T1 - An extended continuation problem for bifurcation analysis in the presence of constraints. AU - Dankowicz, Harry. AU - Schilder, Frank. PY - /1/1. Y1 - /1/1. N2 - This paper presents an extended formulation of the basic continuation problem Cited by: Finally, using bifurcation analyses and numerical continuation techniques [80][81] [82], we study the effect of ecological and environmental gradients represented by changing model parameters on.both of these methods as continuation methods.

The techniques based on predictor and corrector steps and exploiting diﬁerentiability are referred to as \predictor-corrector continuation methods". The techniques based on piece-wise linear approximations are referred to as \piecewise linear continuation .