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

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HAVOC

Aprope

Science Networks. Historical StudiesFor parameter dependent nonlinear Γ-equivariant dynamical systems ., along a branch of Γ-symmetric equilibria {(.,λ(.)) : .∈ .} the Jacobians .share the Γ-equivariance with .(.,λ): ..(Here Γ is a compact Lie group of orthogonal .x .-matrices).

ARM

Alaa Hamada,Sandro C. Esteves,Ashok AgarwalA numerical method for the detection and continuation of homoclinic and heteroclinic orbits is developed for the case of biparametric dynamical systems in two and three dimensions. We formulate a continuation problem for which the regularity conditions are studied. The numerical method is applied to several systems, some of them well-known.

命令變成大炮

Eigenvalue Problems with the Symmetry of a Group and Bifurcations,For parameter dependent nonlinear Γ-equivariant dynamical systems ., along a branch of Γ-symmetric equilibria {(.,λ(.)) : .∈ .} the Jacobians .share the Γ-equivariance with .(.,λ): ..(Here Γ is a compact Lie group of orthogonal .x .-matrices).

容易懂得

A Method for Homoclinic and Heteroclinic Continuation in Two and Three Dimensions,A numerical method for the detection and continuation of homoclinic and heteroclinic orbits is developed for the case of biparametric dynamical systems in two and three dimensions. We formulate a continuation problem for which the regularity conditions are studied. The numerical method is applied to several systems, some of them well-known.

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Understanding Steady-State Bifurcation Diagrams for a Model Reaction-Diffusion System,ions, with the Sel’kov model as a specific example. Apart from the usual linear analysis, other useful analytical tools are scaling laws and singularity theory. On the numerical side we discuss the use of spectral collocation methods.

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amputation

The Numerical Detection of Hopf Bifurcation Points,aviour can occur. This Hopf bifurcation is characterised by the linearisation about a steady state solution possessing a purely imaginary pair of eigenvalues. The cheap and reliable detection of such bifurcation is not however straightforward. The present paper examines the problem and suggests various strategies for solving it.