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A major challenge in forest management is to balance the competing interests of different users. The conservation of biological diversity is an important goal when managing forests in an ecologically sustainable way, but this overlooks aspects of sustainability in terms of urban development and other land use. This research examines physical and biological processes leading to changes in the spatial and temporal land cover on the Curonian Spit, in Lithuania, pre- and post-1990 when the political situation changed heralding new practices. Specifically, the levels of cover categorised as vegetation, sand, forest, urban and grassland are determined using remote sensing images over the period 1989–2017. An assessment of the accuracy of the analysis, when compared with Google Earth, other images and in situ data, produces a high level of confidence in the results. The analysis indicates that the overall forest cover initially decreased until 2009, but since then it has increased by over 1% per year. No urban growth is observed. These and other results are displayed graphically. The forestation of moving dunes, the human impact on the area and changes in the environment are all discussed. The results demonstrate how remote sensing and GIS methods can be used as an important tool for planners, dispensing with the need for costly field trips.

Scaling laws are used to model how different quantifiable properties of cities, such as the number of road traffic accidents or average house prices, vary as a function of city population size, with parameters estimated from data. Arcaute et al. raised the issue of whether specific cities with extremely large population sizes, known as dragon-kings, should be considered separately from other smaller cities when estimating the scaling law parameters since the two types of cities tend to display different behaviour. Through the analysis of randomly generated samples, we find that the inclusion of dragon-kings in the scaling analysis does not affect the estimated values for the parameters but only provided that all the data points satisfy the same scaling law. We also analyse randomly generated samples where data corresponding to a particular city deviates from the scaling law followed by the rest of the cities. We then show that deviations corresponding to dragon-king cities have the most significant effect on the estimated values of the scaling parameters. The extent of this effect also depends on which estimation procedure is used. Our results have important implications on the suitability of scaling laws as a model for urban systems.

Social media posts incorporate real-time information that has, elsewhere, been exploited to predict social trends. This paper considers whether such information can be useful in relation to crime and fear of crime. A large number of tweets were collected from the 18 largest Spanish-speaking countries in Latin America, over a period of 70 days. These tweets are then classified as being crime-related or not and additional information is extracted, including the type of crime and where possible, any geo-location at a city level. From the analysis of collected data, it is established that around 15 out of every 1000 tweets have text related to a crime, or fear of crime. The frequency of tweets related to crime is then compared against the number of murders, the murder rate, or the level of fear of crime as recorded in surveys. Results show that, like mass media, such as newspapers, social media suffer from a strong bias towards violent or sexual crimes. Furthermore, social media messages are not highly correlated with crime. Thus, social media is shown not to be highly useful for detecting trends in crime itself, but what they do demonstrate is rather a reflection of the level of the fear of crime.

Graphical abstract, Discrete observations from data which are obtained from sparse, and yet concentrated events are often observed (e.g. road accidents or murders). Traditional methods to compute summary statistics often include placing the data in discrete bins but for this type of data this approach often results in large numbers of empty bins for which no function or summary statistic can be computed. Here, a method for dealing with sparse and concentrated observations is constructed, based on a sequence of non-overlapping bins of varying size, which gives a continuous interpolation of data for computing summary statistics of the values for the data, such as the mean. The method presented here overcomes the problem which sparsity and concentration present when computing functions to represent the data. Implementation of the method presented here is facilitated via open access to the code. • A new method for computing functions over sparse and concentrated data is constructed. • The method allows straightforward functions to be computed over partitions of the data, such as the mean, but also more complicated functions, such as coefficients, ratios, correlations, regressions and others.

Millions of road traffic collisions take place every year, leading to significant knock-on effects. Many of these traffic collisions take place in urban areas, where traffic levels can be elevated. Yet, little is known about the extent to which urban population size impacts road traffic collision rates. Here, we use urban scaling models to analyse geographic and road traffic collision data from over 300 European urban areas in order to study this issue. Our results show that there is no significant change in the number of road traffic collisions per person for urban areas of different sizes. However, we find individual urban locations with traffic collision rates which are remarkably high. These findings have the potential to inform policies for the allocation of resources to prevent road traffic collisions across the different cities.

Objectives Generally speaking, crime is, fortunately, a rare event. As far as modelling is concerned, this sparsity of data means that traditional measures to quantify concentration are not appropriate when applied to crime suffered by a population. Our objective is to develop a new technique to measure the concentration of crime which takes into account its low frequency of occurrence and its high degree of concentration in such a way that this measure is comparable over time and over different populations. Methods This article derives an estimate of the distribution of crime suffered by a population based on a mixture model and then evaluates a new and standardised measurement of the concentration of the rates of suffering a crime based on that distribution. Results The new measure is successfully applied to the incidence of robbery of a person in Mexico and is able to correctly quantify the concentration crime in such a way that is comparable between different regions and can be tracked over different time periods. Conclusions The risk of suffering a crime is not uniformly distributed across a population. There are certain groups which are statistically immune to suffering crime but there are also groups which suffer chronic victimisation. This measure improves our understanding of how patterns of crime can be quantified allowing us to determine if a prevention policy results in a crime reduction rather than target displacement. The method may have applications beyond crime science.

Different patterns in the incidence of road accidents are revealed when considering areas with increased levels of urbanization. To understand these patterns, road accident data from England and Wales is explored. In particular, the data are used to (i) generate time series for comparison of the incidence of road accidents in urban as opposed to rural areas, (ii) analyse the relationship between the number of road accidents and the population size of a set of urban areas, and (iii) model the likelihood of suffering an accident in an urban area and its dependence with population size. It is observed that minor and serious accidents are more frequent in urban areas, whereas fatal accidents are more likely in rural areas. It is also shown that, generally, the number of accidents in an urban area depends on population size superlinearly, with this superlinear behaviour becoming stronger for lower degrees of severity. Finally, given an accident in an urban area, the probability that the accident is fatal or serious decreases with population size and the probability that it is minor, increases sublinearly. These findings promote the question as to why such behaviours exist, the answer to which will lead to more sustainable urban policies.

In both historical and modern conflicts, space plays a critical role in how interactions occur over time. Despite its importance, the spatial distribution of adversaries has often been neglected in mathematical models of conflict. In this paper, we propose an entropy-maximising spatial interaction method for disaggregating the impact of space, employing a general notion of ‘threat’ between two adversaries. This approach addresses a number of limitations that are associated with partial differential equation approaches to spatial disaggregation. We use this method to spatially disaggregate the Richardson model of conflict escalation, and then explore the resulting model with both analytical and numerical treatments. A bifurcation is identified that dramatically influences the resulting spatial distribution of conflict and is shown to persist under a range of model specifications. Implications of this finding for real-world conflicts are discussed.

A torsion vibration isolator with quasi-zero stiffness (QZS) is proposed to attenuate the transmission of torsional vibration along a shaft system, which also plays a role of coupling between shafts. A pre-compressed cam–roller mechanism is designed to provide torsional negative stiffness that counteracts with the positive torsion stiffness of the vulcanized rubber between shafts. With the design parameters are set to satisfy a unique condition, the stiffness of the isolator delivers a QZS property about the equilibrium position. A nonlinear mathematical model is developed and its dynamic characteristics are further analyzed by using the Harmonic Balance method. A typical folded resonance curve occurs when the vibration amplitude is plotted as the excitation frequency is varied, illustrating a jump phenomenon in the response. The efficiency of vibration attenuation is estimated under a designed torque load, showing that the torsion QZS vibration isolator outperforms the corresponding linear counterpart, especial in low frequency ranges. Furthermore, the torque transmissibility of the QZS isolator is also studied to demonstrate the performance of the QZS isolator when the actual torque deviates from the design load.

Motivated by the dynamics of a trimaran, an investigation of the dynamic behaviour of a double forcing parametrically excited system is carried out. Initially, we provide an outline of the stability regions, both numerically and analytically, for the undamped linear, extended version of the Mathieu equation. This paper then examines the anticipated form of response of our proposed nonlinear damped double forcing system, where periodic and quasiperiodic routes to chaos are graphically demonstrated and compared with the case of the single vertically-driven pendulum.

This article points out a number of key failures of existing practice for building design and then promotes a new approach based upon advances made in the modelling of complex systems and systems engineering. This new approach involves the identification of building functions and modelling techniques to evaluate the performance of a building with respect to a range of criteria in different domains (e.g. spatial, structural, social, environmental, cognitive, organizational, and operational). A systems approach to building design has received limited acceptance to date but can be used to highlight inherent hierarchies and interdependencies between building subsystems, which have traditionally been viewed as being independent. There is currently little agreement as to how the design of different building subsystems should be best integrated in order to satisfy a large range of diverse building functions. Treating the building as a complex system, whereby the interaction of entities produces emergent behaviou...

We aim to move beyond the idea of art as a tool for communicating science, towards a truly interdisciplinary practice where art and public engagement are a fundamental part of the way that science is carried out as promoted by the FuturICT project. Artistic exploration can have a scientific impact when artists act as designers, catalyzers and coordinators of experiments, which scientists interpret and respond to. We propose the creation of a travelling show, consisting of a set of core exhibits and ‘living experiments’: interactive, evolving pieces which blend artistic experience and scientific research. We also propose the creation of a new production oriented, distributed, inter-institutional research centre, focused on developing parallel relations between artistic practice and diverse fields of science. All these initiatives will be aligned with different areas of the FuturICT project, using different aspects of the Living Earth Simulator, Planetary Nervous System, and Knowledge Accelerator to support the creation of rich, interactive, collaborative experiences and in close contact with the educational and participatory platforms of FuturICT.

This paper reviews how concepts and techniques of system dynamics are being applied in new ways to analyse the operations and formation of artificial and societal systems and then to make decisions about them. The ideas and modelling methods to describe natural and technological systems are mostly reductionist (or ‘bottom-up’) and based on general scientific principles, with ad-hoc elements for any particular system. But very complex and large systems involving science, technology and society, whose complete descriptions and predictions are impossible, can still be designed, controlled and managed using the methods of system dynamics, where they are focused on the outputs of the system in relation to the input data available, and relevant external influences. For many complex systems with uncertain behaviour, their models typically combine concepts and methods of bottom-up system dynamics with statistical modelling of past or analogous data and optimization of outputs. System dynamics that has been generalized by advances in mathematical, scientific and technological research over the past 50 years, together with new approaches to the use of data and ICT, has led to powerful qualitative verbal and schematic concepts as well as improved quantitative methods, both of which have been shown to be of great assistance to decisions, notably about different types of uncertainty and erratic behaviour. This approach complements traditional decision-making methods, by introducing greater clarity about the process, as well as providing new techniques and general concepts for initial analysis, system description – using data in non-traditional ways – and finally analysis and prediction of the outcomes, especially in critical situations where system behaviour cannot be analysed by traditional decision-making methods. The scientific and international acceptance of system methods can make decision-making less implicit, and with fewer cultural assumptions. Topical examples of systems and decision-making are given.

This contribution reflects on the comments of Peter Allen [1], Bikas K. Chakrabarti [2], Peter Erdi [3], Juval Portugali [4], Sorin Solomon [5], and Stefan Thurner [6] on three White Papers (WP) of the EU Support Action Visioneer (www.visioneer.ethz.ch). These White Papers are entitled “From Social Data Mining to Forecasting Socio-Economic Crises” (WP 1) [7], “From Social Simulation to Integrative System Design” (WP 2) [8], and “How to Create an Innovation Accelerator” (WP 3) [9]. In our reflections, the need and feasibility of a “Knowledge Accelerator” is further substantiated by fundamental considerations and recent events around the globe. newpara The Visioneer White Papers propose research to be carried out that will improve our understanding of complex techno-socio-economic systems and their interaction with the environment. Thereby, they aim to stimulate multi-disciplinary collaborations between ICT, the social sciences, and complexity science. Moreover, they suggest combining the potential of massive real-time data, theoretical models, large-scale computer simulations and participatory online platforms. By doing so, it would become possible to explore various futures and to expand the limits of human imagination when it comes to the assessment of the often counter-intuitive behavior of these complex techno-socio-economic-environmental systems. In this contribution, we also highlight the importance of a pluralistic modeling approach and, in particular, the need for a fruitful interaction between quantitative and qualitative research approaches. newpara In an appendix we briefly summarize the concept of the FuturICT flagship project, which will build on and go beyond the proposals made by the Visioneer White Papers. EU flagships are ambitious multi-disciplinary high-risk projects with a duration of at least 10 years amounting to an envisaged overall budget of 1 billion EUR [10]. The goal of the FuturICT flagship initiative is to understand and manage complex, global, socially interactive systems, with a focus on sustainability and resilience.

Herd behaviour in financial markets is a recurring phenomenon that exacerbates asset price volatility, and is considered a possible contributor to market fragility. While numerous studies investigate herd behaviour in financial markets, it is often considered without reference to the pricing of financial instruments or other market dynamics. Here, a trader interaction model based upon informational cascades in the presence of information thresholds is used to construct a new model of asset price returns that allows for both quiescent and herd-like regimes. Agent interaction is modelled using a stochastic pulse-coupled network, parametrised by information thresholds and a network coupling probability. Agents may possess either one or two information thresholds that, in each case, determine the number of distinct states an agent may occupy before trading takes place. In the case where agents possess two thresholds (labelled as the finite state-space model, corresponding to agents’ accumulating information over a bounded state-space), and where coupling strength is maximal, an asymptotic expression for the cascade-size probability is derived and shown to follow a power law when a critical value of network coupling probability is attained. For a range of model parameters, a mixture of negative binomial distributions is used to approximate the cascade-size distribution. This approximation is subsequently used to express the volatility of model price returns in terms of the model parameter which controls the network coupling probability. In the case where agents possess a single pulse-coupling threshold (labelled as the semi-infinite state-space model corresponding to agents’ accumulating information over an unbounded state-space), numerical evidence is presented that demonstrates volatility clustering and long-memory patterns in the volatility of asset returns. Finally, output from the model is compared to both the distribution of historical stock returns and the market price of an equity index option.

Humans are inherently mobile creatures. The way we move around our environment has consequences for a wide range of problems, including the design of efficient transportation systems and the planning of urban areas. Here, we gather data about the position in space and time of about 16 000 individuals who uploaded geo-tagged images from locations within the UK to the Flickr photo-sharing website. Inspired by the theory of Lévy flights, which has previously been used to describe the statistical properties of human mobility, we design a machine learning algorithm to infer the probability of finding people in geographical locations and the probability of movement between pairs of locations. Our findings are in general agreement with official figures in the UK and on travel flows between pairs of major cities, suggesting that online data sources may be used to quantify and model large-scale human mobility patterns.

Estimating the critical points at which complex systems abruptly flip from one state to another is one of the remaining challenges in network science. Due to lack of knowledge about the underlying stochastic processes controlling critical transitions, it is widely considered difficult to determine the location of critical points for real-world networks, and it is even more difficult to predict the time at which these potentially catastrophic failures occur. We analyse a class of decaying dynamic networks experiencing persistent failures in which the magnitude of the overall failure is quantified by the probability that a potentially permanent internal failure will occur. When the fraction of active neighbours is reduced to a critical threshold, cascading failures can trigger a total network failure. For this class of network we find that the time to network failure, which is equivalent to network lifetime, is inversely dependent upon the magnitude of the failure and logarithmically dependent on the threshold. We analyse how permanent failures affect network robustness using network lifetime as a measure. These findings provide new methodological insight into system dynamics and, in particular, of the dynamic processes of networks. We illustrate the network model by selected examples from biology, and social science.

This paper considers a parametrically excited pendulum whose symmetry is destroyed by a bias term. This study investigates the effect of this symmetry-breaking by comparing the control parameter space of frequency and amplitude of the forcing with its symmetric counterpart. Approximate bifurcation analysis is used to predict the new escape boundary using a harmonic balance scheme. The bifurcations exhibited in the asymmetrical model are echoed in the case of the tilted pendulum, whose drive is not quite vertical. The experimental importance of this alteration is furthermore discussed with a view of predicting the onset of rotating motions. More specifically, an easily viewed drop in amplitude experienced by the asymmetric oscillatory solution may be considered as the trigger of escape and can therefore be regarded as a precursor of imminent danger or operational difficulties. The paper goes on to examine the impact that a variation in the bias term causes in terms of the changes to the region of safe, oscillatory motion. Applications in ship dynamics give a physical significance of this papers findings.

A planar pendulum is considered which is parametrically excited by a periodic vertical force. The amplitude and frequency of the excitation are used as control parameters. The downward, hanging and the upward, inverted positions correspond to equilibrium positions if we only consider the variation in angle measured from the downward position. For moderate levels of forcing, there are zones that exist in the space of control parameters, where the downward hanging position is unstable and initial conditions that are close to the hanging position lead to steady state oscillations of period-2. To review this situation, this paper describes the development of these oscillations as the amplitude of forcing is varied. In the largest zone, a symmetry-breaking occurs which brings about a pair of asymmetric oscillations. This break in symmetry of the period-2 solution can lead to either an increase or decrease in the amplitude of the forthcoming swing and reference to the experimental significance of this angle change is noted in this paper. Typically, further increases of the parameter produce a cascade of period doubling bifurcations, before most oscillating solutions eventually lose their stability so that the system must experience a rotation. As a result, symmetry-breaking becomes an effective precursor to escape from the local potential well around the hanging position. Here we compare this behaviour with that in other resonance zones. The change of geometric structure when the symmetry-breaking bifurcation occurs is examined and graphically represented as a ‘pinched’ cylinder-like shape, compared with the Mobius strip that has been associated with the period-doubling bifurcation. The paper also refers to practical problems, where the introduction of nonlinearity means that potentially all frequencies below the main zone of the control space lead to dangerous effects and in some scenarios disastrous outcomes.

We present a so-called zero-crossing identification method that can crack the security shell of the chaotic encryption method [Chaos, Solitons & Fractals 19 (2004) 919] with periodic modulation. By collecting a special set of truncated data from the zero-crossing incidents of the modulated signal, we can detect the modulating function from chaotic signal. Furthermore we extend the technique to extract modulating function from noise and discuss the potential applications of this method in engineering.

We consider the dynamics of impact oscillators with multiple degrees of freedom subject to more than one motion limiting constraint or stop. A mathematical formulation for modeling such systems is developed using a modal approach including a modal form of the coefficient of restitution rule. The possible impact configurations for an N degree of freedom system are considered, along with definitions of the impact map for multiply constrained systems. We consider sticking motions that occur when a single mass in the system becomes stuck to an impact stop, and discuss the computational issues related to computing such solutions. Then using the example of a two degree of freedom system with two constraints we describe exact modal solutions for the free flight and sticking motions which occur in this system. Numerical examples of sticking orbits for this system are shown and we discuss identifying the region, S in phase space where these orbits exist. We use bifurcation diagrams to indicate differing regimes of vibro-impacting motion for two different cases; firstly when the stops are both equal and on the same side (i.e. the same sign) and secondly when the stops are unequal and of opposing sign. For these two different constraint configurations we observe qualitatively different dynamical behavior, which is interpreted using impact mappings and two-dimensional parameter space.

A great number of studies have shown the complex nonlinear dynamics of mechanical systems with repeated normal impacts. An oblique frictional impact introduces even more complicated dynamics such as stick-slip motions to those systems. Hence, the dynamics of oblique vibro-impacting systems with possible sliding motion is an open problem. Based on a hybrid analysis of vibro-impact dynamics, kinematics and complementary conditions, a piecewise analysis method is developed in the paper to describe the sliding motion during an oblique impact. Thereby, a parametrically excited planar pendulum between two parallel rigid walls is studied as an illustrative example. The example, together with the corresponding numerical results, shows that the sliding impacts occur in such a system with a set of properly selected parameters.

We consider oscillatory, nonrotating periodic solutions of the parametrically excited pendulum. We determine the zones in the parameter space in which different types of oscillatory solutions are realized. In particular we determine the zones in which the T-periodic and 2T-periodic harmonic and subharmonic oscillatory solutions are the dominant type of stable solutions. The symmetry properties of these solutions and the associated scenarios of transition to tumbling chaos are also discussed.

Computer simulations of spin waves parametric excitations are carried out in the framework of the two modes model. The dependence of the auto-oscillation (AO) frequency, f, on the pumping amplitude h is investigated. The results support the expression of Lvov et al. for this dependence in cases when the parametric excitation threshold, h th is very close to the auto-oscillation threshold h osc . In cases when h osc is considerably larger than h th , a much better fit is obtained to a slightly modified expression: f = f 0 + B([h/h osc ] 2 -1) 0.5 where f 0 is the onset frequency and B is a constant. Support is given to the idea of Lvov et al. that auto oscillation evolves from an oscillation that is damped below h osc and becomes self sustained at h osc . We find that τ CO , the decay time of AO below h osc exhibits a critical slowing down power law: τ CO α (1 - h/h osc ) -2.2 . The dependence of f on the inter mode interaction strengths when h is constant, satisfies the expression: f = D + C/(E + 2T 11 + S 11 + 2T 12 + S 12 ) where D, C, and E are constants and T 11 , T 12 , S 11 , and S 12 are the inter mode interaction strengths. This result supports the conjecture that the dependence of the auto-oscillation frequency on the physical parameters is very similar to that of N 0 , the steady state value of the total number of parametric excitations.

Non-smooth modelling techniques have been successfully applied to lumped mass-type structures for modelling phenomena such as vibro-impact and friction oscillators. In this paper, the application of these techniques to continuous elements using the example of a cantilever beam is considered. Employing a Galerkin reduction to form an N -degree-of-freedom modal model, a technique for modelling impact phenomena using a non-smooth dynamics approach is demonstrated. Numerical simulations computed using the non-smooth model are compared with experimentally recorded data for a flexible beam constrained to impact on one side. A method for dealing with sticking motions when numerically simulating the beam motion is presented. In addition, choosing the dimension of the model based on power spectra of experimentally recorded time series is discussed.

A new theoretical scheme is presented to model the shape of a sand dune at equilibrium that does not require iterative calculations of the interaction between the wind flow and topography. The model is constructed by incorporating theory based on aerodynamics into a grain-scale model that estimates the shear velocity at the dune crest through the calculation of the sand trapping efficiency of the slipface in the lee of the dune. Published field data, collected in southern Peru, California and southern Morocco, show that as a dune becomes higher the windward slope becomes steeper. For the model proposed, the wind flow over a dune was first assumed to be similar to that over a Gaussian hill. By further assuming a fixed shear velocity on the level surface, the windward slope angle and migration speed of dunes in southern Peru can be explained. To comply with all available data, some aspects are still open to further investigation. However the theoretical insight presented herein implies that the upper limit of dune height may be greater in windier environments.

The shape and migration speed of a proto-dune are mathematically discussed. The migration speed of a low dune is shown to be inversely proportional to its wind-directional length. Proto-dunes, whose wind-directional lengths are about 10 m, are expected to migrate at finite speeds. Copyright (C) 2002 John Wiley Sons, Ltd.

We introduce an approach to detect cyclical patterns embedded within chaotic data and make use of the detected patterns to estimate periodic-like motions in a chaotic process. A chaotic attractor contains many unstable periodic orbits (UPOs). The UPOs are hidden cyclical patterns that dominate the dynamical evolution of the system. Knowledge of UPOs can be used for estimating the trends of chaotic evolutions. A numerical experiment is conducted to illustrate an application on the business cycle detection.

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.

The increasing usage of social media for conversations, together with the availability of its data to researchers, provides an opportunity to study human conversations on a large scale. Twitter, which allows its users to post messages of up to a limit of 140 characters, is one such social media. Previous studies of utterances in books, movies and Twitter have shown that most of these utterances, when transcribed, are much shorter than 140 characters. Furthermore, the median length of Twitter messages was found to vary across US states. Here, we investigate whether the length of Twitter messages varies across different regions in the UK. We find that the median message length, depending on grouping, can differ by up to 2 characters.

We use experimentally recorded time series of impact times to calculate the interspike intervals of an impacting oscillator. Using the interspike intervals we analyse the dynamics and especially the periodicity exhibited by the oscillator. We evaluate the effect of noise in the measurements and how this is reflected in the interspike intervals and the subsequent analyses, We compare experimental data against results produced numerically. (C) 2001 Elsevier Science Ltd. All rights reserved.

We consider the dynamics of a two-degree of freedom impact oscillator subject to a motion limiting constraint. These systems exhibit a range of periodic and nonperiodic impact motions. For a particular set of parameters, we consider the bifurcations which occur between differing regimes of impacting motion and in particular those which occur due to a grazing bifurcation. Unexpected resonant behavior is also observed, due to the complexity of the dynamics. We consider both periodic and chaotic chatter motions and the regions of sticking which exist. Finally we consider the types of chaotic motion that occur within the parameter range. We discuss the possibility in relating successive low velocity impacts, especially with respect to possible low dimensional mappings for such a system.

A fundamental issue in crime prevention is the efficient deployment of resources and the effective targeting of interventions, both of which require some form of prediction of future crime. One crime for which this is feasible is burglary, the distinctive spatio-temporal signatures of which can be exploited to inform predictions. Mathematical models in particular are capable of both encoding concisely the theoretical foundations of criminal behaviour and allowing the quantitative analysis of specific scenarios, and their capacity to reproduce the general patterns of burglary suggests that the approach has considerable potential. Previous models, however, are situated on simplified representations of space and do not reflect realistically the built environment in which crime takes place; specifically, they do not incorporate urban street networks. Such networks are fundamental to situational theories of crime, in the sense that they determine the configuration of urban space and, therefore, shape those human activity patterns which are thought to give rise to crime. Furthermore, streets are the natural domain for many policing activities, and their structure is determined by planning decisions, so that insight into their relationship with crime is likely to be of immediate practical use. With this in mind, this paper presents a mathematical model of crime which is explicitly situated on a street network. After discussing theoretical considerations and specifying the model itself, examples of typical networks are explored.

In this work multi-modal systems subject to impact are considered. Using energy balance techniques for an arbitrary contact interval the effects of modal vibration can be included. The energy balance is used to obtain a relationship between the coefficient of restitution and the modal energy during the contact period. This allows the effects of impact induced vibration to be considered. The subsequent analytical relationships demonstrate that increasing contact duration and excitation of higher modes can reduce the effective value of the coefficient of restitution. It is also shown how this approach can be related to work on energetically consistent impacts.

When considering the synchronisation of two identical coupled systems the threshold of stability of a synchronised state is determined by the sign of the largest transverse Lyapunov exponent. In this Letter, we report simple cases in which analytic representations for the threshold of stability of the synchronised state are obtainable, but are not in agreement with numerics. This phenomenon is roundoff induced, and is investigated for coupled iterative maps that, in some cases, can be described as homogeneous diffusion processes.

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.

The dynamics of a vibro-impacting cantilever beam experiment using an impact load cell is considered. The signal recorded from the cell produces spike train -type data. The issues related to the analysis of such data are discussed; particularly the sampling rate and threshold values. For vibro-impact motion of the beam, the duration of impacts is investigated by using a time of contact measure. The implications are discussed for vibro-impact systems mathematically modelled by using instantaneous impact assumptions (coefficient of restitution). Using the load cell to measure impact forces for the beam system is also considered. Then a delay reconstruction of the dynamics of the system by using interspike intervals is considered. It is demonstrated how this process is effected by the influence of noise and the data-acquision process using numerical simulations of the experimental data. It is shown how simple periodic motions can be identified by using a probability density approach and possible future research is highlighted.

We consider the transient time to synchronisation in unidirectionally coupled dynamical systems, both discrete maps and continuous flows. We note that while in certain systems the time distribution is typical of chaotic transients, in other cases the distribution possesses a specific spatial organization.

We consider here the dynamics of a planar pendulum whose pivot points is rapidly forced with a periodic driving. We focus attention on stable `inverted' motions which exist on, or close to, the upright position. Following earlier studies, the initial emphasis is placed on the system with vertical sinusoidal forcing while the later results correspond to excitation which has an additional horizontal component. In particular we examine the nature of the stable inverted solution as the symmetry is broken via numerical investigations. Finally, some remarks are made on the physical significance of the results.

The dynamics of a simple dynamical system subjected to an elastic restoring force, viscous damping and dry friction forces is investigated. Self-sustained oscillations occur with non-standard attracting properties. Discontinuity of the governing equations leads to non-standard bifurcations, which are studied here, with analytical and numerical tools.

It appears that fires in buildings are inevitable. All too often they lead to loss of life and large costs in repairing damage to a building's structure and contents. There is a clear need not only...

Inverted oscillations of a parametrically driven planar pendulum are considered, together with their relationship to the inverted solution. In particular, a horseshoe structure of the associated manifolds is identified which explains the similarity between the bifurcations of the inverted position and the hanging position. This allows us to apply a large body of existing knowledge to the dynamics enabling a lower bound on the forcing required to achieve inverted oscillations to be established.

Methods developed for the control of chaos usually consider a nonlinear system set at particular parameters which result in chaotic motion. Then, using only tiny control adjustments, a chaotic trajectory is stabilised onto a choice of unstable periodic solutions embedded within the original chaotic motion. In this paper however we make use of the periodic windows, which typically exist within the chaotic regimes of a bifurcation diagram as a single parameter is varied, so that the same advantages of chaos control can be achieved, but now with the system initially set at parameters which produce a stable periodic motion. Within a periodic window an infinite number of unstable solutions may naturally coexist with the stable state. By perturbing the stable motion a chaotic-like transient can be induced which, when it approaches the location of a desired solution, can be stabilised. We illustrate the feasibility of this idea using a self-locating control scheme in a periodic window of the Henon map. We show that, starting from a stable periodic motion, one can flexibly manipulate the system between many co-existing solutions without major changes to the overall configuration of the system

The study of dynamical systems is of significant practical importance. We investigate here the concept of the safe basin and the use of the amplitude/frequency of forcing parameters plane which can be applied to a wide range of dynamical systems including control applications. A computer aided study of the performance of such systems using Matlab/Simulink with a Watcom C/C++ compiler is illustrated. The technique is easy to use and is only limited by the properties of the Matlab/Simulink programme in which the system is simulated. The behaviour of a pressure transducer is used as a simple example; as a further example the stab ility and robustness of a practical control strategy, designed to control chaotic behaviour, has also been investigated.