Titlebook: Continuation and Bifurcations: Numerical Techniques and Applications; Dirk Roose,Bart De Dier,Alastair Spence Book 1990 Kluwer Academic Pu

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亲爱

Use of Approximate Inertial Manifolds in Bifurcation Calculations,of the flow of the PDE to the inertial manifold is given by a finite set of ODEs called an inertial form, which captures all the long time dynamic behavior of the PDE. We give a brief survey of several numerical schemes to approximate inertial manifolds and hence inertial forms. We then implement th

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Bifurcations, Chaos and Self-Organization in Reaction-Diffusion Systems,ight of recent advances in nonlinear mathematics. Chaos and mixed-mode oscillations in far- from-equilibrium chemical reactions are first described. We show how homoclinic tangencies of Sil’nikov type and associated to a cycle can help us in elucidating the complex bifurcation sequences and the rela

暗指

Steady-State/Steady-State Mode Interaction in Nonlinear Equations with Z2-Symmetry,uivariance) condition. Specifically we analyze the solution structure near a point where a path of symmetry-breaking bifurcations and a path of fold points intersect. The treatment is such that numerical information is obtained which could prove useful when switching from one path to another.

衍生

Symbolic Computation and Bifurcation Methods,y, for the calculation of bifurcation points. However, analytical methods are frequently needed to characterize the bifurcation, being also a valuable guide for the numerical approach. As in the effective application of bifurcation methods the hand calculation of very long expressions is normally re

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Accord

产生

Global Bifurcations and their Numerical Computation,periodic orbits at a homoclinic orbit. In this paper we extend our numerical approach to connecting orbits and the error analysis developed in [1]. The basic nondegeneracy condition is characterized by a geometric transversality condition. Further, the analysis of the error obtained by truncating to