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A computer based technique has been developed to test the performance of complex nonlinear systems, using Matlab/Simulink™ and C/C++. In this approach a dynamic system, represented by its mathematical model, is stimulated by a sequence of sinusoidal signals and the system stability is observed by a stability diagram. Furthermore the technique is developed to test the degree of accuracy and sensitivity of transducers. Such devices are complicated nonlinear, closed-loop, systems in their own right. In this paper the long term stability of a typical pressure transducer model with hard and soft spring effects is examined. The range of use is determined by a shaded stability diagram. In addition performance of a micromachined, silicon, accelerometer is examined. Important properties of the accelerometer such as the degree of accuracy and sensitivity are considered

Results of a numerical investigation are presented of the behaviour of a mathematical model which approximates the response of a thin metal strip, or beam, held vertically and clamped at its base, which is driven to impact against a motion limiting constraint. Previous theoretical analyses, in conjunction with numerical studies, have highlighted the complicated dynamics that the system exhibits following a single or series of grazing bifurcations. Under certain conditions subharmonic solutions and chaotic impacting motions are unavoidable. These solutions, which involve several impacts per orbital period introducing relatively large impact velocities, have been viewed experimentally. Meanwhile research into the control of chaos, in which unstable orbits embedded within chaotic motions are stabilized, has advanced over recent years. New control methods have been developed and experimentally implemented. The present work brings these two fields together for the first time. Numerical evidence is given for the use of control to eliminate complicated motions by tracking lower periodic solutions. The stabilized motions near the grazing incidence have lower impact velocities than the naturally existing stable solutions leading to a significant reduction of the impact force which may have significant engineering relevance.

A design aid developed in a Matlab/Simulink environment is presented which may be used given to examine the dynamic behaviour of nonlinear systems. The degree of stability of a system is determined by the control space basin. In the case of a disturbance the transient motion of the system is observed from a range of initial conditions. The technique is extended to enable the investigation of the accuracy and sensitivity of closed loop analogue and digital transducers.

This paper describes computational methods for the evaluation of safe limits of operation of driven mechanical systems. We define the problem of evaluating the safety of transient and steady-state motions in terms of the escape from a potential well. We then describe a simple, robust method of determining boundaries of safe operation in control space, and we conclude by applying the method to a number of examples.

We present a simple mathematical model to replicate the key features of the sterile insect technique (SIT) for controlling pest species, with particular reference to the mosquito Aedes aegypti, the main vector of dengue fever. The model differs from the majority of those studied previously in that it is simultaneously spatially explicit and involves pulsed, rather than continuous, sterile insect releases. The spatially uniform equilibria of the model are identified and analysed. Simulations are performed to analyse the impact of varying the number of release sites, the interval between pulsed releases and the overall volume of sterile insect releases on the effectiveness of SIT programmes. Results show that, given a fixed volume of available sterile insects, increasing the number of release sites and the frequency of releases increases the effectiveness of SIT programmes. It is also observed that programmes may become completely ineffective if the interval between pulsed releases is greater that a certain threshold value and that, beyond a certain point, increasing the overall volume of sterile insects released does not improve the effectiveness of SIT. It is also noted that insect dispersal drives a rapid recolonisation of areas in which the species has been eradicated and we argue that understanding the density dependent mortality of released insects is necessary to develop efficient, cost-effective SIT programmes.

Wave induced set-up is a process that leads to increased water levels in coastal regions. When coupled with storm conditions, wave set-up – or, for brevity, set-up – can significantly increase the risk of flooding or structural damage and therefore is of particular importance when considering coastal management or issues related to the planning of nearshore infrastructures. Here, we investigate the effects of set-up in the coastal region of the Gulf of Finland in the Baltic Sea, close to Tallinn, Estonia, although the results will have wider relevance for many other areas. Due to a lack of continuous wave data we employ modelling to provide input data using a calculation scheme based on a high-resolution (470 m) spectral wave model WAM to replicate spatial patterns of wave properties based on high-quality, instrument-measured wind data from the neighbourhood of the study site. The results indicate that for the specific geometry of coastline under consideration, there is a variation in set-up which is strongly affected by wind direction. The maximum set-up values are up to 70–80 cm in selected locations. This is more than 50% of the all-time maximum water level and thus may serve as a substantial source of marine hazard for several low-lying regions around the city. Wind directions during storms have changed in recent years and, with climate variability potentially increasing, these results will encourage further tests which may be used in a policy setting regarding defences or other structures in and around coastlines. In particular, with urban development now taking place in many coastal regions (including the one within this study) these results have implications for local planners. They may also be incorporated into new storm warning systems.

In estimating how economic growth depends on various inputs, economists commonly use long periods of data encompassing both main extremes to fluctuations in the economy: recession and expansion. Here we focus on recession years because during expansion even countries with bad economic policies may experience large growth. Specifically, we study how growth depends on the proportion of public-sector workforce, p and competitiveness, quantified by the Global Competitiveness Index, GCI. For the 2008-2011 economic downturn and for 57 countries, we find that the growth rate of GDP per capita, g, decreases with p, and increases with ΔGCI. Further, more competitive countries attract more foreign direct investments per capita, I, than less competitive countries, where I is proportional to GCI(α). We propose a production function, divided into the private and public sectors, where GDP depends on market capitalization, the public (private)-sector workforce, and competitiveness level, used to quantify the public sector efficiency.

In August 2011, several areas of London experienced episodes of large-scale disorder, comprising looting, rioting and violence. Much subsequent discourse has questioned the adequacy of the police response, in terms of the resources available and strategies used. In this article, we present a mathematical model of the spatial development of the disorder, which can be used to examine the effect of varying policing arrangements. The model is capable of simulating the general emergent patterns of the events and focusses on three fundamental aspects: the apparently-contagious nature of participation; the distances travelled to riot locations; and the deterrent effect of policing. We demonstrate that the spatial configuration of London places some areas at naturally higher risk than others, highlighting the importance of spatial considerations when planning for such events. We also investigate the consequences of varying police numbers and reaction time, which has the potential to guide policy in this area.

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.

This paper presents a nonlinear magnetic low-frequency vibration isolator designed with the characteristic of quasi-zero stiffness (QZS). An approximate expression of the magnet repulsive force is proposed and a unique analytical relationship between the stiffness of vertical spring and initial gap settings of the magnet springs is derived for the QZS system. Based on the harmonic balance (HB) method, the force transmissibility is formulated and the jumping frequencies, effect of excitation force and damping ratio are discussed for characteristic analysis. An experimental prototype is developed and tested. The performance of the QZS system is verified through a series of experimental studies showing that the new model greatly outperforms standard linear isolation systems especially in low-frequency domain. The tuning techniques for adapting to the change of loading mass and adjusting the QZS property in practice are also addressed.

The parametrically driven pendulum exhibits a large variety of stable periodic and chaotic motions, together with the hanging and inverted equilibrium states. These motions can be oscillatory, rotational or a combination of these. The asymptotic solution depends crucially upon the initial conditions imparted to the system for a given frequency and amplitude of forcing, used here as parameters. The existence of a large chaotic attractor has been numerically and experimentally verified, which persists for a reasonably broad range of the parameters. This chaotic solution is referred to as a tumbling motion since it includes rotations in both clockwise and anticlockwise directions, as well as oscillations about the hanging position. Embedded within the corresponding attractor is an infinite number of unstable periodic solutions which may be classified according to the number of oscillations or rotations within a given number of periods of the periodic driving force. In this paper, the topological theory of dynamical systems is used to pinpoint the location in parameter and phase space of desired orbits. Numerical procedures can then be readily applied to refine this information and a simple control algorithm applied to stabilize this unstable orbit. The initial theoretical approach provides greater flexibility in enabling the system to achieve a variety of different periodic states by small adjustments of the driving frequency. Remarks are also made regarding experimental implementation.

This paper provides new insight into the dynamical response of an impacting driven beam. A simple mathematical model utilising a coefficient of restitution rule captures qualitative (and limited quantitative) behaviour of an experimental apparatus allowing the parameter space to be divided into zones according to their behaviour type. Emphasis is directed towards identifying the zones which separate regular period-1 impacting solutions from irregular, apparently chaotic, impacting and non-impacting motions.

Oscillatory solutions for the parametrically excited pendulum are considered, and comparison is made between the pendulum and systems that permit escape from a symmetric potential well. Unstable and stable orbits are identified and located in control space by considering the horseshoe formed by the invariant manifolds of the hilltop saddles at 0 = ±n, and employing methods of symbolic dynamics. Observing the tangencies in the manifolds from these saddles allows considerable detail regarding the bifurcational structure of the system to be determined without recourse to lengthy simulations. Estimation of changes in the Birkhoff signature additionally permits estimates of escape for systems with symmetric and asymmetric potential wells. These numerical/analytical results can prove to be very useful in estimating global dynamics which may in the future be employed in experimental systems.

A nonlinear dynamical system in a chaotic state is very sensitive to errors. Inherent noise in physical systems gives rise to difficulties for stabilizing chaotic systems onto desired unstable periodic orbits, particularly with large eigenvalues. The idea of adjusting the system state more frequently to eliminate error deviations from a desired orbit is utilized and given in variational form for flows. This control scheme acting on multiple sections can cope with relatively large noise levels. A Duffing oscillator and a parametrically excited pendulum are used in numerical studies. The relationship between controllable noise levels and the number of control sections is discussed.

In an earlier work a deterministic model, FIRE-SPRINT A1, which predicts the conditions for fire spread in a tunnel, has been presented. The model, based on the concepts of non-linear dynamics, may be used to predict the conditions for spread from one vehicle to another in a tunnel fire. A few illustrative simulations were given. In this communication the results of further simulations are presented; in particular, bifurcation following has been conducted for the case of fire spread from one heavy goods vehicle to another in a rail tunnel. These demonstrate further how the model may be used to identify those geometrical and thermo-physical conditions which give rise to instability and a jump. In principle, such a model may be used as an aid to design and operation for a tunnel.

We consider the application of topological methods (such as knot, braid and Nielsen-Thurston theory) to transient, rather than periodic, orbits of periodically-forced nonlinear oscillators. The methods are restricted to systems with a three-dimensional phase space.

An algorithm is introduced, based on the Newton method, to stabilize chaotic systems onto a desired periodic orbit utilizing the feedback of an output sequence on accessible parameters. The method does not necessarily rely on explicit knowledge of the system dynamics and only an approximate location of the desired periodic orbit is required which can subsequently be automatically and accurately detected in the control process. The algorithm is locally stable, has a fast convergence rate, is applicable to arbitrary dimensional systems, and is suitable for experimental situations. In numerical simulations, a pair of periodically forced, coupled Duffing oscillators is investigated, which produce a 4-D system.

A method is considered for locating oscillating, nonrotating solutions for the parametrically-excited pendulum by inferring that a particular horseshoe exists in the stable and unstable manifolds of the local saddles. In particular, odd-periodic solutions are determined which are difficult to locate by alternative numerical techniques. A pseudo-Anosov braid is also located which implies the existence of a countable infinity of periodic orbits without the horseshoe assumption being necessary.

Stabilization of chaotic dynamical systems onto periodic orbits is considered via a control approach based on the contraction-mapping theorem. The convergence of the control scheme is guaranteed by the construction of a contraction map. The control time required to reach within a finite precision of the desired state is in a logarithmic form, which can be adjusted by setting the convergence rate. The effects of noise on the control process are investigated; in particular (a) the effect on the magnitude of control inputs, which determines the condition of a controllable noise level, and (b) the effect on the robustness of the control process. The Cubic map is used to numerically demonstrate the control process.

A nonlinear model for simulating the heave-roll motions of ships in following waves is presented. The parametric excitation is modeled by a Hill's type equation, instead of the conventional Mathieu's equation. The model includes not only the linear but also the quadratic coupling term. Instability conditions for parametrically excited rolling motions are derived using the harmonic balance method. The results are verified by numerical analyses. The effects of including the quadratic coupling term on the instability conditions and nonlinear responses are studied. The complex dynamic behaviour of the coupled system in the various instability regions is also investigated. Bifurcations of the flip, fold and pitchfork types are observed in the Poincare mapping of the numerically simulated responses. Chaotic motions leading to boundary crises and inevitable capsize are also reported.

A heteroclinic tangency marking the initial change in secondary Birkhoff signature is identified as a good indicator of the chaotic escape from a symmetric potential well under parametric excitation as it occurs shortly after the symmetry breaking bifurcation which precedes the final event. This is compared to the criterion for asymmetric potential wells, and the lack of any change in primary Birkhoff signature highlights the differences in the two cases.

In this paper we consider the behavior of a two degree-of-freedom mechanical system incorporating static and dynamic friction, assumed to be a decreasing function of the relative sliding velocity. The model consists of two blocks linked by springs, which ride upon a moving belt. The dynamics of the system are described within a four-dimensional phase space. A three-dimensional Poincaré map is discussed together with a simpler one-dimensional map of a scalar variable. Considering the one-dimensional map it is possible to study all the attractors of the system for small belt velocities including the construction of one-dimensional basins of attraction. Thus, albeit in a partial zone of the control-phase space, the global dynamics of the system can be characterized displaying periodic, quasi-periodic and chaotic oscillations.

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.

A comparison between the predictions from a previously derived non-dimensional fire growth model and experimental data obtained from a series of fire experiments in a scale (0.4 m cube) compartment is made. Both the qualitative and quantitative types of theoretical behaviour appear to be in reasonable agreement with those found experimentally.

A non-linear model of fire in a tunnel, FIRE-SPRINT A1, is presented. It predicts the conditions for fire spread from one object to another within a tunnel which has longitudinal ventilation. It does this by identfying unstable states within the system and associating instability with the onset of fire spread. The particular case of spread from an initial fire to a heavy goods vehicle (HGV) within the Channel Tunnel is considered as an illustration. Thereby the thermo-physical and geometrical conditions leading to such a jump may be elucidated.

The European Physical Journal Special Topics, 214 (1), ISSN:1951-6355, ISSN:1951-6401

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 country's GDP and the predisposition of its inhabitants to look forward., Scientific Reports, 2, ISSN:2045-2322

This paper considers the issues around managing large sci-entific projects, and draws conclusions for the governance and man-agement of FuturICT, based on previous experience of Big Science projects, such as CERN and ATLAS. We also consider the legal and ethical issues of the FuturICT project as the funding instrument moves from the Seventh Framework Programme to Horizon 2020.

The European Physical Journal Special Topics, 214 (1), ISSN:1951-6355, ISSN:1951-6401

Society depends decisively on the availability of infrastructure systems such as energy, telecommunication, transportation, banking and finance, health care and governmental and public administration. Even selective damages of one of these infrastructures may result in disruptions of governmental, industrial or public functions. Vulnerability of infrastructures therefore provides spectacular leverage for natural disasters as well as criminal and terrorist actions. Threats and risks are part of the technological, economical, and societal development. This article focuses on the development and characterization of an integrative risk-management which, from the perspective of “resilient systems”, can be seen as an innovative and pro-active crisis management approach dealing with the increasing amount of complexity in societies in a comprehensive, agile and adaptive way.

WOS:000312246900010 (Nº de Acesso Web of Science) “Prémio Científico ISCTE-IUL 2013” Education is a major force for economic and social wellbeing. Despite high aspirations, education at all levels can be expensive and ineffective. Three Grand Challenges are identified: (1) enable people to learn orders of magnitude more effectively, (2) enable people to learn at orders of magnitude less cost, and (3) demonstrate success by exemplary interdisciplinary education in complex systems science. A ten year 'man-on-the-moon' project is proposed in which FuturICT's unique combination of Complexity, Social and Computing Sciences could provide an urgently needed transdisciplinary language for making sense of educational systems. In close dialogue with educational theory and practice, and grounded in the emerging data science and learning analytics paradigms, this will translate into practical tools (both analytical and computational) for researchers, practitioners and leaders; generative principles for resilient educational ecosystems; and innovation for radically scalable, yet personalised, learner engagement and assessment. The proposed Education Accelerator will serve as a 'wind tunnel' for testing these ideas in the context of real educational programmes, with an international virtual campus delivering complex systems education exploiting the new understanding of complex, social, computationally enhanced organisational structure developed within FuturICT.

This paper describes a method that can direct a chaotic dynamical system to achieve a desired state by adjusting parameters within an optimal control process. The well-known discrete-time Henon system is chosen to illustrate the method which can steer a chaotic trajectory towards a stable fixed point, force a stable fixed point into a chaotic attractor, or switch from one chaotic attractor into another chaotic attractor.

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.

This paper considers the behaviour of a two degree-of-freedom autonomous system with static and dynamic friction consisting of two blocks linked by springs on a moving belt. This system is the simplest model which has been used to simulate the dynamics of seismic faults. The friction force is assumed to be a decreasing function of the relative sliding velocity. The motion of the blocks is composed of a uniform stick motion, during which the divergence of the system is zero, and an accelerated slip motion, during which the divergence is positive. The mathematical model by definition concentrates the dissipation on the point where the slip motion ceases. It is assumed that slip occurs only in one direction. A three-dimensional Poincare map and a scalar single variable map are discussed which characterize the dynamics of the system in a simple way. The one-dimensional map can be used to diagnose the chaotic behaviour of the full system, and quantities, similar to Lyapunov exponents, can be easily calculated which provide information regarding the system-sensitive dependence on initial conditions. The system dynamics illustrate the idea of studying the earthquake generation mechanism as a chaotic phenomenon.

Bifurcational precedences are obtained for systems which permit escape from a potential well by considering the three striped horseshoe formed by the invariant manifolds of the hilltop saddles. Considerable information regarding the bifurcational structure is obtained by considering the crossings of periodic orbits in an idealised suspension of the flow in terms of this three striped horseshoe.

The two analytical methods employs to give approximations to the escape zone both yield reasonable results. The harmonic balance method is the more accurate, especially at high frequency, but the critical velocity criterion does have the advantage of producing a closed form analytical expression for the zone rather than solving a series of non-linear equations numerically. While both methods give good results, it is also worth noting that although stable non-rotating solutions exist below the escape zone, their basins of attractions may be fractal, and subject to rapid basin erosion. The onset of fractal basin boundaries and the possibility of rapid basin erosion may be predicted by a Melnikov analysis as in reference.

The parametrically excited pendulum exhibits a wide variety of non-linear behaviour. We consider numerical studies of periodic motion; the simple periodic solutions are also studied analytically using the harmonic balance method. For more complicated motions the problem is tackled by solving algebraic non-linear equations either using the definition of fixed points for Poincare map, or, where convenient, using a Galerkin technique; in both techniques the stability of solutions can also be checked. The cell mapping technique is used to study the attracting basins and to systematically assess the various types of periodic motions.

The ultimate goal of the FuturICT Flagship is to understand and manage complex, global, socially interactive systems, with a focus on sustainability and resilience. Revealing the hidden laws and processes underlying societies constitutes the most pressing scientific grand challenge of our century. Integrating the three components of ICT, Complexity Science and the Social Sciences will lead to a paradigm shift, facilitating a symbiotic co-evolution of ICT and society. Data from our complex globe-spanning ICT system will be leveraged to develop models of techno-socio-economic systems. In turn, insight from these models will inform the development of a new generation of socially adaptive, self-organised ICT systems. FuturICT as a whole will act as a Knowledge Accelerator, turning massive data into knowledge and technological progress. FuturICT will create the scientific methods and ICT platforms needed to address planetary-scale challenges and opportunities in the 21st century. Specifically, FuturICT will build a sophisticated simulation, visualization and participation platform, known as the Living Earth Simulator. This platform will power Observatories, to detect and mitigate crises, and Participatory Platforms, to support decision-making for policy-makers and citizens. In the Coordination Action Pilot Study which is running from May 2011-April 2012, activities will take place to develop the scientific vision and roadmap, secure stakeholder commitment, establish the FuturICT legal and operational infrastructure, and build on our remarkable success in uniting previously fragmented research communities. The main aim of the activities throughout the project will be to refine the FuturICT vision and identify measureable milestones along the way. This will produce an ambitious large-scale, science-driven, visionary research initiative to promote and develop future research outcomes in ICT. Through these activities, the Coordination Action will allow Europe to grasp this unique opportunity for groundbreaking progress in science and ICT, with great impacts for society, governance and industry by launching the FuturICT Flagship in 2013.

The problem of calculating the response of cable structures to static loads is considered. The proposed method is based on the principle of the conservation of energy and the minimization of the energy-work functional. The solution is achieved by the conjugate gradients method. The mathematical aspects of the method are briefly presented. Experimental tests for a static load on a circular saddle-shaped cable net model are presented in tabular form and are compared with the analytical findings.

Similarities in the bifurcation diagrams of three systems that permit escape from a potential well under parametric excitation are related to horseshoe formation in the invariant manifolds of the hill-top saddles.

This paper considers the behaviour of a mechanical oscillator with cubic non-linearity subjected to a forcing excitation whose frequency remains constant while the amplitude is ramped, growing until it reaches a predetermined value. We concentrate on the nature of the basins of attraction whose size indicates the stability of the system, in a structural sense. The reduced level of forecing at the initial stages of ramping produces a delay in bifurcational events when compared to the constant sinusoidally forced counterpart. Preliminary results show that for some parameter values the area of basin does not increase monotonically as the length of ramping is varied.

The configuration factor for thermal radiation from a section of the ceiling of a tunnel or the inner surface of a partial cylinder to a point on the axis has been derived. Calculations indicate the possibility of high incident radiative heat fluxes from the ceiling to the center. Configuration factors have been calculated for a column furnace used for fire resistance testing.

The behaviour of a hardening Duffing oscillator subjected to narrow band random excitation is examined. The influence of possible jumps, between competing states, on the probability distribution of the response amplitude is addressed. A quasi-harmonic approximation of system behaviour is adopted which is capable of reproducing the observed concave shape of probability functions and compares well with predictions obtained via stochastic averaging techniques and with digital simulations.

The problem of estimating the probability distribution of the response amplitude of a hardening Duffing oscillator subjected to narrow band excitation is addressed. A method is presented which is based on a quasi-static approximation of system behaviour and is capable of reproducing the resulting concave shape of probability functions when a jump phenomenon occurs. Predictions are compared with those obtained via stochastic averaging techniques and with digital simulations.

This paper examines the dynamical behavior of fire growth within a building or more simply a compartment. Simplified equations are derived to study the development of a fire. The transient fire growth is modelled using concepts of nonlinear dynamical systems theory, and the effect of ventilation is considered. Emphasis is placed on qualitative behavior with a view to understanding the phenomena involved in fire growth, with specific attention focused on highly dangerous flashover conditions.

A comparison between experimental data and both the qualitative and quantitative nonlinear behavior predicted by a fire growth model is made for a model compartment (0·4 m cube). The predictions are in relatively good agreement with the data, and are consistent with the expected nonlinear behaviour and in particular the occurrence of flashover jumps.

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.