Steven R. Bishop

Quantifying the Advantage of Looking Forward

We introduce a future orientation index to quantify the degree to which Internet users worldwide seek more information about years in the future than years in the past. We analyse Google logs and find a striking correlation between the countrys GDP and the predisposition of its inhabitants to look forward.

Dynamical Complexities of Forced Impacting Systems

The model of a forced linear oscillator with instantaneous impacts at one or two stops is discussed. The nonlinearities introduced by the instantaneous impact rule are sufficient to cause typical nonlinear behaviour. The impact rule is discontinuous, introducing discontinuities into discrete time Poincaré maps defined from the continuous time dynamical system. Discontinuities also exist in the derivatives of these maps. The implications of these discontinuities are discussed and their relevance to engineering applications is assessed with suggestions for further research.

Bifurcations in impact oscillations

Models of impact oscillators using an instantaneous impact law are by their very nature discontinuous. These discontinuities geve rise to bifurcations which cannot be classified using the usual tools of bifurcation analysis. However, we present numerical evidence which suggests that these discontinuous bifurcations are just the limits (in some sense) of standard bifurcations of smooth dynamical systems as the impact is hardened. Finally we show how one dimensional maps of the interval with essentially similar characteristics can exhibit the same kinds of bifurcational behaviour, and how these bifurcations are related to standard bifurcations.

Manipulating the scaling factor of projective synchronization in three-dimensional chaotic systems

Scaling factor characterizes the synchronized dynamics of projective synchronization in partially linear chaotic systems but it is difficult to be estimated. To manipulate projective synchronization of chaotic systems in a favored way, a control algorithm is introduced to direct the scaling factor onto a desired value. The control approach is derived from the Lyapunov stability theory. It allows us to arbitrarily amplify or reduce the scale of the response of the slave system via a feedback control on the master system. In numerical experiments, we illustrate the application to the Lorenz system. (c) 2001 American Institute of Physics.

Rotating periodic orbits of the parametrically excited pendulum

Rotating orbits in the parametrically excited pendulum are considered. The location of subharmonic orbits shows that there is in general no easily defined lower bound on the forcing amplitude, p, below which rotating orbits cannot exist. This is particularly important if the parametrically excited pendulum is considered in terms of escape from a potential well.

Fractal basins and chaotic bifurcations prior to escape from a potential well

The escape of a periodically driven damped oscillator from a potential well is intimately associated with homoclinic tangles, fractal basins, and a variety of chaotic bifurcations. A bifurcation diagram, including an analytical Melnikov solution is presented for a canonical asymmetric cubic potential, and comparisons are made with recent results for the Holmes two-well oscillator.

Simulation of the effect of wind speedup in the formation of transverse dune fields

A computer simulation model for transverse-dune-field dynamics, corresponding to a uni-directional wind regime, is developed. In a previous formulation, two distinct problems were found regarding the cross-sectional dune shape, namely theerosionintheleeofdunesandthesteepnessofthewindwardslopes.Thefirstproblemissolvedbyintroducingnoerosion inshadowzones.Thesecondissueisovercomebyintroducingawindspeedup(shearvelocityincrease)factor,whichcanbe accountedforbyaddingatermtotheoriginaltransportlength,whichisproportionaltothesurfaceheight.Byincorporating these features we are able to model dunes whose individual shape and collective patterns are similar to those observed in nature.Moreoverweshowhowtheintroductionofanon-linearshear-velocity-increasetermleadstothereductionofdune height,andthismayresultinanequilibriumdunefieldconfiguration.Thisisthoughttobebecausethenon-linearincreaseof thetransportlengthmakesthesandtrappingefficiencylowerthanunity,evenforhigherdunes,sothattheincomingandthe outgoingsandfluxareinbalance.Tofullydescribetheinter-dunemorphologymoreprecisedynamicsintheleeofthedune must be incorporated. Copyright # 2000 John Wiley & Sons, Ltd.

Modelling desert dune fields based on discrete dynamics

A mathematical formulation is developed to model the dynamics of sand dunes. The physical processes display strong non-linearity that has been taken into account in the model. When assessing the success of such a model in capturing physical features we monitor morphology, dune growth, dune migration and spatial patterns within a dune field. Following recent advances, the proposed model is based on a discrete lattice dynamics approach with new features taken into account which reflect physically observed mechanisms.

Nonlinear dynamics of flashover in compartment fires

Flashover is a phenomenon whereby a room fire undergoes a rapid increase in size and intensity. Such a transition is suggestive of a nonlinear process. We therefore seek to apply modern geometrical and computational techniques of nonlinear dynamics to a simplified model of fire growth to investigate flashover and other instabilities occuring in compartment fires. We present here a simplified model of fire growth in a compartment and conduct a preliminary analysis of the dynamics exhibited, in terms of both transient simulations and quasi-steady evolution manifolds, for variations in controlling parameters.

Quantifying the digital traces of Hurricane Sandy on Flickr.

Society’s increasing interactions with technology are creating extensive “digital traces” of our collective human behavior. These new data sources are fuelling the rapid development of the new field of computational social science. To investigate user attention to the Hurricane Sandy disaster in 2012, we analyze data from Flickr, a popular website for sharing personal photographs. In this case study, we find that the number of photos taken and subsequently uploaded to Flickr with titles, descriptions or tags related to Hurricane Sandy bears a striking correlation to the atmospheric pressure in the US state New Jersey during this period. Appropriate leverage of such information could be useful to policy makers and others charged with emergency crisis management.