2 edition of **Numerical Bifurcation Analysis for Reaction-Diffusion Equations** found in the catalog.

- 364 Want to read
- 28 Currently reading

Published
**2000**
by Springer Berlin Heidelberg in Berlin, Heidelberg
.

Written in English

- Mathematics,
- Numerical analysis,
- Global analysis (Mathematics)

This book provides the readers numerical tools for a systematic analysis of bifurcation problems in reaction- diffusion equations. Emphasis is put on combination of numerical analysis with bifurcation theory and application to reaction-diffusion equations. Many examples and figures are used to illustrate analysis of bifurcation scenario and implementation of numerical schemes. The reader will have a thorough understanding of numerical bifurcation analysis and the necessary tools for investigating nonlinear phenomena in reaction-diffusion equations.

**Edition Notes**

Statement | by Zhen Mei |

Series | Springer Series in Computational Mathematics -- 28, Springer Series in Computational Mathematics -- 28 |

Classifications | |
---|---|

LC Classifications | QA297-299.4 |

The Physical Object | |

Format | [electronic resource] / |

Pagination | 1 online resource (xiv, 414 p.) |

Number of Pages | 414 |

ID Numbers | |

Open Library | OL27077973M |

ISBN 10 | 3642086691, 3662041774 |

ISBN 10 | 9783642086694, 9783662041772 |

OCLC/WorldCa | 851382178 |

In this paper we present computational techniques to investigate the solutions of two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD systems, and extend them to operate on large-scale meshes for arbitrary surfaces. In particular, we use spectral techniques for a linear stability analysis to. Numerical methods of reaction-diffusion equations and systems; Turing Pattern: (a) Fish pattern A reaction–diffusion wave on the skin of the marine angelfish Pomacanthus Shigeru Kondo & Rihito Asai, Nature , (31 August ).

However, we conjecture that only the first Hopf bifurcation at ; 0 is super-critical and that the subsequent ones are subcritical, thus generating unstable periodic orbits. Finally, we note that to the best of our knowledge all examples for Hopf bifurcation in reaction-diffusion equations are obtained for systems rather than for a single equation. The paper presents the numerical analysis of a finite volume-element method for solving the unsteady scalar reaction-diffusion equations. The main idea of the method is to combine the concepts that are employed in the finite volume and the finite element method together. The finite volume method is used to discretize the unsteady.

Reaction-Diffusion Systems, Dynamical Systems, Numerical Bifurcation Theory, Mathematical Physiology (cellular physiology and systems physiology), Cardiac Cell Dynamics, Neurodynamics, Jamology, Traffic Jam, Pedestrian Dynamics, Mathematical Modelling of . May 10, · Nonlinear Differential Equations: Invariance, Stability, and Bifurcation presents the developments in the qualitative theory of nonlinear differential equations. This book discusses the exchange of mathematical ideas in stability and bifurcation simplicityhsd.com Edition: 1.

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However, an analytical bifurcation analysis is possible only for exceptional cases. This book is devoted to nu merical analysis of bifurcation problems in reaction-diffusion equations. The aim is to pursue a systematic investigation of generic bifurcations and mode interactions of Author: Zhen Mei.

This monograph is the first to provide readers with numerical tools for a systematic analysis of bifurcation problems in reaction-diffusion equations. Readers will gain a thorough understanding of numerical bifurcation analysis and the necessary tools for investigating nonlinear.

"This book provides the readers numerical tools for a systematic analysis of bifurcation problems in reaction-diffusion equations. Emphasis is put on combination of numerical analysis with bifurcation theory and application to reaction-diffusion equations.

Buy Numerical Bifurcation Analysis for Reaction-Diffusion Equations (Springer Series in Computational Mathematics) on simplicityhsd.com FREE SHIPPING on qualified ordersCited by: Dhooge A, Govaerts W, Kuznetsov YA () Matcont: A Matlab package for numerical bifurcation analysis of ODE's.

ACM TOMS 29, pp – Mei Z () Numerical Bifurcation Analysis for Reaction-Diffusion Equations. Springer, Doedel EJ, Keller HB, Kernevez JP () Numerical Analysis and Control of Bifurcation Problems (II.

jor practical issues of applying the bifurcation theory to ﬁnite-dimensional problems. This new edition preserves the structure of the ﬁrst edition while updating the context to incorporate recent theoretical developments,in particular,new and improved numerical methods for bifurcation analysis.

The treatment of some topics has been clariﬁed. Introduction. Among the rich numerical bifurcation analysis toolbox, continuation techniques are efficient numerical schemes to compute solution manifolds of nonlinear systems and determine attractors as a function of model parameters for discretized partial differential equations (PDEs).Cited by: 1.

Reaction–diffusion systems are mathematical models which correspond to several physical phenomena. The most common is the change in space and time of the concentration of one or more chemical substances: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out over a surface in space.

Bifurcation Analysis of Reaction-Diffusion Equations. Multiply Periodic Travelling Waves. Such equations are often called reaction-diffusion equations (or interaction-diffusion equations. Asymptotic modelling in fluid mechanics: proceedings of a symposium in honour of Professor Jean-Pierre Guiraud, held at the Université Pierre et Marie Curie, Paris France, April /.

It is not meaningful to talk about a general theory of reaction-diffusion systems. This is a rela-tively recent subject of mathematical and applied research. Most of the work that has been done so far is concerned with the exploration of particular aspects of very speciﬁc systems and equations.

On the Numerical Analysis of the Imperfect Bifurcation of codim. This monograph is the first to provide readers with Numerical tools for a systematic analysis of bifurcation problems in reaction-diffusion equations.

Many examples and figures illustrate analysis of bifurcation scenario and implementation of Numerical schemes. Readers will gain a thorough understanding of Numerical bifurcation analysis and the necessary tools for investigating nonlinear. We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations.

We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the simplicityhsd.com by: 1.

Nonlinear Differential Equations: Invariance, Stability, and Bifurcation presents the developments in the qualitative theory of nonlinear differential equations. This book discusses the exchange of mathematical ideas in stability and bifurcation theory.

In this paper the structure of the nonnegative steady-state solutions of a system of reaction-diffusion equations arising in ecology is investigated. The equations model a situation in which a pred Cited by: SIAM Journal on Applied MathematicsAbstract | PDF ( KB) () Exponential decay toward equilibrium via entropy methods for reaction–diffusion simplicityhsd.com by: Instabilities, Bifurcation, and Fluctuations in Chemical Systems.

Cover: Instabilities, Bifurcation, and Fluctuations in Chemical Systems. Share this book. Additional Subjects. Instabilities, Bifurcation, and Fluctuations in Chemical Systems Bifurcation Analysis of Reaction-Diffusion Equations IV.

Size Dependence (Giles Auchmuty). Reactiondiffusion equations.Spatial Ecology Via Reaction Diffusion Equations eBooks Spatial Ecology Via Reaction Diffusion Equations is available on PDF, ePUB and DOC format.

Abstract and Applied Analysis supports the. Numerical Bifurcation Analysis for Reaction-Diffusion Equations. Spatial Ecology via Reaction-Diffusion. A Mathematical model to Solve Reaction Diffusion Equation using Differential Transformation Method Rahul Bhadauria#1, A.K.

Singh*2, D.P Singh#3 #13Department of Mathematics, RBS College, Agra, India #2Departmaent of Mathematics, FET RBS College, Agra, India Abstract— The present work is designed for differential.

In this paper, we present an algorithm for deriving the normal forms of Bautin bifurcations in reaction-diffusion systems with time delays and Neumann boundary conditions.

On the center manifold near a Bautin bifurcation, the first and second Lyapunov coefficients are calculated explicitly, which completely determine the dynamical behavior near the bifurcation simplicityhsd.com: Yuxiao Guo, Ben Niu.Chapter 8 The Reaction-Diffusion Equations Reaction-diffusion (RD) equations arise naturally in systems consisting of many interacting components, (e.g., chemical reactions) and are widely used to describe pattern-formation phenomena in variety of biological, chemical and physical sys-tems.We are interested in wave-pinning in a reaction-diffusion model for cell polarization proposed by simplicityhsd.com, simplicityhsd.come and simplicityhsd.comein-Keshet.

They showed interesting bifurcation diagrams and stability results for stationary solutions for a limiting equation by numerical computations. Kuto and Tsujikawa showed several mathematical bifurcation results of stationary solutions of this simplicityhsd.com by: 3.