Numerical Bifurcation Analysis for Reaction-Diffusion Equations
Title | Numerical Bifurcation Analysis for Reaction-Diffusion Equations PDF eBook |
Author | Zhen Mei |
Publisher | Springer Science & Business Media |
Pages | 422 |
Release | 2013-03-09 |
Genre | Mathematics |
ISBN | 3662041774 |
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 phenomena in reaction-diffusion equations.
Stability and Bifurcation Analysis of Reaction-diffusion Systems with Delays
Title | Stability and Bifurcation Analysis of Reaction-diffusion Systems with Delays PDF eBook |
Author | Rui Hu |
Publisher | |
Pages | 276 |
Release | 2009 |
Genre | |
ISBN |
Numerical Continuation and Bifurcation in Nonlinear PDEs
Title | Numerical Continuation and Bifurcation in Nonlinear PDEs PDF eBook |
Author | Hannes Uecker |
Publisher | SIAM |
Pages | 380 |
Release | 2021-08-19 |
Genre | Mathematics |
ISBN | 1611976618 |
This book provides a hands-on approach to numerical continuation and bifurcation for nonlinear PDEs in 1D, 2D, and 3D. Partial differential equations (PDEs) are the main tool to describe spatially and temporally extended systems in nature. PDEs usually come with parameters, and the study of the parameter dependence of their solutions is an important task. Letting one parameter vary typically yields a branch of solutions, and at special parameter values, new branches may bifurcate. After a concise review of some analytical background and numerical methods, the author explains the free MATLAB package pde2path by using a large variety of examples with demo codes that can be easily adapted to the reader's given problem. Numerical Continuation and Bifurcation in Nonlinear PDEs will appeal to applied mathematicians and scientists from physics, chemistry, biology, and economics interested in the numerical solution of nonlinear PDEs, particularly the parameter dependence of solutions. It can be used as a supplemental text in courses on nonlinear PDEs and modeling and bifurcation.
Bifurcation: Analysis, Algorithms, Applications
Title | Bifurcation: Analysis, Algorithms, Applications PDF eBook |
Author | KÜPPER |
Publisher | Birkhäuser |
Pages | 368 |
Release | 2013-03-08 |
Genre | Science |
ISBN | 3034872410 |
The conference on BIFURCATIONS: ANALYSIS, ALGORITHMS, APPLICATIONS took place in Dortmund in August 18 - 22, 1986. More then 150 Scientists from 16 countries participated in the meeting, among them mathematicians, engi neers, and physicists. A broad spectrum of new results on bifurcation was covered by 49 talks. The diversity of the range of treated topics and of involved fields inspired fruitful discussions. 36 refereed papers are contained in these proceedings. The subjects covered treat bifurcation problems, ranging from theoretical investigations to numerical results, with emphasis placed upon applications. The more theoreti cal papers include the topics symmetry breaking, delay differential equations, Cornu spirals, homoclinic orbits, and selfsimilarity. Different kinds of bifurcations are treated: Hopf bifurcation, bifurcation from continuous spec trum, complex bifurcation, and bifurcation near tori. Several numerical as pects are discussed, among them continuation, block elimination, and spectral methods. Algorithms are proposed for approximating manifolds, calculating pe riodic solutions and handling multi-parameter problems. Ample space is devoted to· applications. Classical phenomena from fluid mechanics (such as convection rolls and th~ Taylor vortex problem), buckling, and reaction-diffusion pro blems are considered. Other applications of bifurcations include railway vehicle dynamics, computer graphics, semiconductors, drilling processes, simu lation of oil reservoirs, and rotor dynamics. The proceedings reflect current research in bifurcation. They are an attempt to bring together researchers from differ~nt disciplines to stimulate common effort towards a better understanding and handling of bifurcation pro blems.
Instabilities, Bifurcations, and Fluctuations in Chemical Systems
Title | Instabilities, Bifurcations, and Fluctuations in Chemical Systems PDF eBook |
Author | L. E. Reichl |
Publisher | University of Texas Press |
Pages | 440 |
Release | 1982-09-01 |
Genre | Science |
ISBN | 029274157X |
Twentieth-century research in the field of chemical pattern formation saw extraordinary progress due to the pathbreaking contributions of Nobel laureate Ilya Prigogine and his co-workers. Evidence exists that the dissipative structures studied by Prigogine and his colleagues may play a dominant role in the processes of self-organization of biological systems, the fundamental phenomena that govern all life forms. Brought together in this valuable volume are topical papers from the this research. Important aspects of nonlinear chemical pattern formation—dissipative structures—in chemical, biochemical, and geological systems are surveyed by leading scientists in the field of nonlinear chemistry. Topics covered include experimental observations of pattern formation in a variety of systems, bifurcation theory and analysis of nonlinear chemical rate equations, and the stochastic theory of nonlinear chemical reactions. Of particular interest are the studies of the effects of electric fields on the determination of nonequilibrium states of chemical systems.
Continuation and Bifurcations: Numerical Techniques and Applications
Title | Continuation and Bifurcations: Numerical Techniques and Applications PDF eBook |
Author | Dirk Roose |
Publisher | Springer Science & Business Media |
Pages | 415 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 9400906595 |
Proceedings of the NATO Advanced Research Workshop, Leuven, Belgium, September 18-22, 1989
Numerical Analysis of Reaction Diffusion Equations
Title | Numerical Analysis of Reaction Diffusion Equations PDF eBook |
Author | Donald J. Estep |
Publisher | |
Pages | |
Release | 1994 |
Genre | Boundary value problems |
ISBN |