摘要:

Models of the interactions between population, economy and environment often contain nonlinear functional relationships and variables that vary at different speeds. These properties foster apparent unpredictabilities in the system behavior. We identify a class of deterministic models on the interaction of demographic, economic and environmental interactions in which catastrophic changes in environmental quality can take place, but involve a delay between passing a critical threshold level of pollution and the final collapse of the environment. We denoted this delay as the 'environmental grace period'. We illustrate the usefulness of geometric singular perturbation theory and local bifurcation theory to analyse such models. In particular, we show how it is possible to obtain analytic expressions for: (1) the level of emissions above which environmental deterioration begins; (2) the time it takes from reaching the critical level of emissions to the beginning of rapid environmental deterioration and (3) the level of emissions at the time that rapid deterioration begins. Because our results are analytic, they make the outcomes of demo- graphic, economic and environmental interactions more predictable and, therefore, poten- tially more manageable.

ISSN:0268-1110    

DOI:10.1080/02681119808806252

出版商:Carfax Publishing Ltd    

年代:1998

数据来源: Taylor

摘要:

We present a special model which is a caricature of the collinear three-body problem. Near triple-collision behavior for the model is governed by the collision manifold. Using the dynamics on the collision manifold, we study the allowed sequences of bounces by generating a partition on a Poincare slice in the flow. When the ratio of masses is small, we use two subshifts of finite type to describe which sequences of bounces are guaranteed and which are excluded. There is a third class of sequences which are neither guaranteed nor excluded. We also describe the bifurcations of this system as the ratio of masses approaches zero.

ISSN:0268-1110    

DOI:10.1080/02681119808806253

出版商:Carfax Publishing Ltd    

年代:1998

数据来源: Taylor

摘要:

We consider how internal symmetries can effect the solutions observed in three symmetrically coupled oscillators due to a symmetry-breaking Hopf bifurcation, and in particular consider three cases where the coupling terms produceorequivariance with respect to an ‘Internal’symmetry. We do this by, first, examining the generic behaviour expected on the respective centre manifolds before interpreting these results as solution branches in systems of coupled oscillators and, finally, presenting some numerical examples. By using the standard techniques, we thus present a specific example of the more general approach of Dionne et al. in a more familiar setting, as well as carrying out additional stability calculations. It turns out that is becomes extremely important how we couple the individual oscillators with respect to the internal symmetry, with thecase producing some quite unexpected results

ISSN:0268-1110    

DOI:10.1080/02681119808806254

出版商:Carfax Publishing Ltd    

年代:1998

数据来源: Taylor

摘要:

A roll-forced pendulum is studied as a rudimentary model for a sea-state driven ship crane in this work. Centripetal acceleration measurements were made in a number of non-resonant forcing conditions. In addition to large-amplitude resonant responses, a variety of beating responses were found in the transient mode; this behavior is significant due to the light damping and thus long influence of the transient dynamics. The (transient as well as steady-state) frequency content of the centripetal acceleration spectrum is predicted and compared to experiment using power spectral methods and spectrograms.

ISSN:0268-1110    

DOI:10.1080/02681119808806255

出版商:Carfax Publishing Ltd    

年代:1998

数据来源: Taylor

ISSN:0268-1110    

DOI:10.1080/02681119808806251

出版商:Carfax Publishing Ltd    

年代:1998

数据来源: Taylor