摘要:

The equivariant Hopf bifurcation theorem of Golubitsky and Stewart (1985) gives sufficient conditions, analogous to the classical Hopf bifurcation theorem, for the existence of periodic solutions to ordinary differential equations with symmetry. They show how to compute the asymptotic stability of these solutions on the assumption that the vector field is in Birkhoff normal form to infinite order. By studying perturbations of the Floquet operator we prove that it is sufficient for the vector to be in Birkhoff normal form to suitably high finite order, which can be achieved by an appropriate change of coordinates. Thus in principle the stability can be calculated without assuming Birkhoff normal form. A similar result has been obtained by Taliaferro (1987) using different methods.

ISSN:0268-1110    

DOI:10.1080/02681118808806035

出版商:Oxford University Press    

年代:1988

数据来源: Taylor

摘要:

A perturbation method is developed for detecting homoclinic connections for the unstable Periodic solution of Duffing's equation with negative linear restoring term. The technique involves a mixture of averaging and singular perturbation methods. Each saddle connection implies a homoclinic point, and the initial bifurcation value of the forcing amplitude is given by the same formula as that obtained by Melnikov's method. The method has also been extended to include an investigation of double loop and transverse saddle connections. Conditions have also been obtained for certain large-amplitude oscillations which are known to occur for this system. The results are illustrated by numerical results for manifolds and saddle connections.

ISSN:0268-1110    

DOI:10.1080/02681118808806036

出版商:Oxford University Press    

年代:1988

数据来源: Taylor

摘要:

The qualitative behaviour of solutions of the neutral delay logistic equationis investigated; sufficient conditions are obtained for the local asymptotic stability of the positive steady state or (*).The osciiiaiory and non-oscinaiory enaracierisucs oi me positive solutions of (*) are also studied.

ISSN:0268-1110    

DOI:10.1080/02681118808806037

出版商:Oxford University Press    

年代:1988

数据来源: Taylor

摘要:

We have characterized a strange attractor with a fractal dimension in a fully-developed turbulent channel flow simulated numerically by computing the Lyapunov dimension based on a spatial correlation concept. Our paper presents an example along the line of current discussions whether we can represent an infinite-dimensional dynamical system (fluid flow) by a small finite-dimensional dynamical system. At least for this particular flow under the specified conditions, we can indeed approximate the fluid system by a small-dimensional dynamical system.

ISSN:0268-1110    

DOI:10.1080/02681118808806038

出版商:Oxford University Press    

年代:1988

数据来源: Taylor

摘要:

The aim of this work is to study some cases of stability ofparticularly in

ISSN:0268-1110    

DOI:10.1080/02681118808806039

出版商:Oxford University Press    

年代:1988

数据来源: Taylor

摘要:

The ‘pooled chemical approximation’ in chemical kinetics, a procedure based originally only on intuition, has already proved an extremely valuable route to predicting the possibility of nonlinear dynamical responses such as oscillations or propagating chemical waves for a variety of simple chemical reaction schemes. The use of this technique requires that the concentrations of some initial reactant species be identified (a) as large compared with those of key reactive intermediates and (b) as changing on a relatively slow timescale, and thus can be regarded as constants or, to a higher approximation, as evolving quasisteadily. Though this approach has been found to be successful for a number of classic models this is not universally the case. Here we report on almost disastrous failure for an otherwise acceptable scheme with mass-action kinetics. We show that the oscillatory behaviour predicted by the pooled chemical approximation does not survive into the full scheme, and perhaps more significantly, when we come to consider the behaviour for large values of the initial concentration of the pooled chemical, we find that the time in which this pooled chemical is used updecreasesas its initial concentration is increased.

ISSN:0268-1110    

DOI:10.1080/02681118808806040

出版商:Oxford University Press    

年代:1988

数据来源: Taylor

摘要:

An algorithm is given to normalize vector fields with nilpotent linear part using representation theory of. The theory is set up in such a way that the whole construction can also be used for Hamiltonian problems, or any other problem where one has a graded Lie algebra setting.

ISSN:0268-1110    

DOI:10.1080/02681118808806041

出版商:Oxford University Press    

年代:1988

数据来源: Taylor

ISSN:0268-1110    

DOI:10.1080/02681118808806034

出版商:Oxford University Press    

年代:1988

数据来源: Taylor