Controlling chaos? The value and the challenges of applying complexity theory to project management

The literature abounds with descriptions of failures in high-profile projects and a range of initiatives has been generated to enhance project management practice (e.g., Morris, 2006). Estimating from our own research, there are scores of other project failures that are unrecorded. Many of these failures can be explained using existing project management theory; poor risk management, inaccurate estimating, cultures of optimism dominating decision making, stakeholder mismanagement, inadequate timeframes, and so on. Nevertheless, in spite of extensive discussion and analysis of failures and attention to the presumed causes of failure, projects continue to fail in unexpected ways. In the 1990s, three U.S. state departments of motor vehicles (DMV) cancelled major projects due to time and cost overruns and inability to meet project goals (IT-Cortex, 2010). The California DMV failed to revitalize their drivers’ license and registration application process after spending $45 million. The Oregon DMV cancelled their five year, $50 million project to automate their manual, paper-based operation after three years when the estimates grew to $123 million; its duration stretched to eight years or more and the prototype was a complete failure. In 1997, the Washington state DMV cancelled their license application mitigation project because it would have been too big and obsolete by the time it was estimated to be finished. There are countless similar examples of projects that have been abandoned or that have not delivered the requirements.

Universal power law in crossover from integrability to quantum chaos

We study models of interacting fermions in one dimension to investigate the crossover from integrability to nonintegrability, i.e., quantum chaos, as a function of system size. Using exact diagonalization of finite-sized systems, we study this crossover by obtaining the energy level statistics and Drude weight associated with transport. Our results reinforce the idea that for system size L -> infinity nonintegrability sets in for an arbitrarily small integrability-breaking perturbation. The crossover value of the perturbation scales as a power law similar to L-eta when the integrable system is gapless. The exponent eta approximate to 3 appears to be robust to microscopic details and the precise form of the perturbation. We conjecture that the exponent in the power law is characteristic of the random matrix ensemble describing the nonintegrable system. For systems with a gap, the crossover scaling appears to be faster than a power law.

Use of polydispersity index as control parameter to study melting/freezing of Lennard-Jones system: Comparison among predictions of bifurcation theory with Lindemann criterion, inherent structure analysis and Hansen-Verlet rule

Using polydispersity index as an additional order parameter we investigate freezing/melting transition of Lennard-Jones polydisperse systems (with Gaussian polydispersity in size), especially to gain insight into the origin of the terminal polydispersity. The average inherent structure (IS) energy and root mean square displacement (RMSD) of the solid before melting both exhibit quite similar polydispersity dependence including a discontinuity at solid-liquid transition point. Lindemann ratio, obtained from RMSD, is found to be dependent on temperature. At a given number density, there exists a value of polydispersity index (delta (P)) above which no crystalline solid is stable. This transition value of polydispersity(termed as transition polydispersity, delta (P) ) is found to depend strongly on temperature, a feature missed in hard sphere model systems. Additionally, for a particular temperature when number density is increased, delta (P) shifts to higher values. This temperature and number density dependent value of delta (P) saturates surprisingly to a value which is found to be nearly the same for all temperatures, known as terminal polydispersity (delta (TP)). This value (delta (TP) similar to 0.11) is in excellent agreement with the experimental value of 0.12, but differs from hard sphere transition where this limiting value is only 0.048. Terminal polydispersity (delta (TP)) thus has a quasiuniversal character. Interestingly, the bifurcation diagram obtained from non-linear integral equation theories of freezing seems to provide an explanation of the existence of unique terminal polydispersity in polydisperse systems. Global bond orientational order parameter is calculated to obtain further insights into mechanism for melting.

Some modified bifurcation problems with application to imperfection sensitivity in buckling

The branching theory of solutions of certain nonlinear elliptic partial differential equations is developed, when the nonlinear term is perturbed from unforced to forced. We find families of branching points and the associated nonisolated solutions which emanate from a bifurcation point of the unforced problem. Nontrivial solution branches are constructed which contain the nonisolated solutions, and the branching is exhibited. An iteration procedure is used to establish the existence of these solutions, and a formal perturbation theory is shown to give asymptotically valid results. The stability of the solutions is examined and certain solution branches are shown to consist of minimal positive solutions. Other solution branches which do not contain branching points are also found in a neighborhood of the bifurcation point.

The qualitative features of branching points and their associated nonisolated solutions are used to obtain useful information about buckling of columns and arches. Global stability characteristics for the buckled equilibrium states of imperfect columns and arches are discussed. Asymptotic expansions for the imperfection sensitive buckling load of a column on a nonlinearly elastic foundation are found and rigorously justified.

Nonlinear Dynamics of Nd:YAG lasers: Hopf bifurcation, Multistability and Chaotic Synchronization

In this thesis we have presented some aspects of the nonlinear dynamics of Nd:YAG lasers including synchronization, Hopf bifurcation, chaos control and delay induced multistability.We have chosen diode pumped Nd:YAG laser with intracavity KTP crystal operating with two mode and three mode output as our model system.Different types of orientation for the laser cavity modes were considered to carry out the studies. For laser operating with two mode output we have chosen the modes as having parallel polarization and perpendicular polarization. For laser having three mode output, we have chosen them as two modes polarized parallel to each other while the third mode polarized orthogonal to them.

Hopf bifurcation in parallel polarized Nd:YAG laser

Dynamics of Nd:YAG laser with intracavity KTP crystal operating in two parallel polarized modes is investigated analytically and numerically. System equilibrium points were found out and the stability of each of them was checked using Routh–Hurwitz criteria and also by calculating the eigen values of the Jacobian. It is found that the system possesses three equilibrium points for (Ij, Gj), where j = 1, 2. One of these equilibrium points undergoes Hopf bifurcation in output dynamics as the control parameter is increased. The other two remain unstable throughout the entire region of the parameter space. Our numerical analysis of the Hopf bifurcation phenomena is found to be in good agreement with the analytical results. Nature of energy transfer between the two modes is also studied numerically.

Onset And Characterisation Of Chaos In A Two Dimensional Nonlinear Deterministic Model

Nature is full of phenomena which we call "chaotic", the weather being a prime example. What we mean by this is that we cannot predict it to any significant accuracy, either because the system is inherently complex, or because some of the governing factors are not deterministic. However, during recent years it has become clear that random behaviour can occur even in very simple systems with very few number of degrees of freedom, without any need for complexity or indeterminacy. The discovery that chaos can be generated even with the help of systems having completely deterministic rules - often models of natural phenomena - has stimulated a lo; of research interest recently. Not that this chaos has no underlying order, but it is of a subtle kind, that has taken a great deal of ingenuity to unravel. In the present thesis, the author introduce a new nonlinear model, a ‘modulated’ logistic map, and analyse it from the view point of ‘deterministic chaos‘.

A perspective on chaos theory: Potential applications to intelligent buildings

Mathematical models have been vitally important in the development of technologies in building engineering. A literature review identifies that linear models are the most widely used building simulation models. The advent of intelligent buildings has added new challenges in the application of the existing models as an intelligent building requires learning and self-adjusting capabilities based on environmental and occupants' factors. It is therefore argued that the linearity is an impropriate basis for any model of either complex building systems or occupant behaviours for control or whatever purpose. Chaos and complexity theory reflects nonlinear dynamic properties of the intelligent systems excised by occupants and environment and has been used widely in modelling various engineering, natural and social systems. It is proposed that chaos and complexity theory be applied to study intelligent buildings. This paper gives a brief description of chaos and complexity theory and presents its current positioning, recent developments in building engineering research and future potential applications to intelligent building studies, which provides a bridge between chaos and complexity theory and intelligent building research.

Bubbling transition to spatial mode excitation in an extended dynamical system

We investigated the transition to spatio-temporal chaos in spatially extended nonlinear dynamical systems possessing an invariant subspace with a low-dimensional attractor. When the latter is chaotic and the subspace is transversely stable we have a spatially homogeneous state only. The onset of spatio-temporal chaos, i.e. the excitation of spatially inhomogeneous modes, occur through the loss of transversal stability of some unstable periodic orbit embedded in the chaotic attractor lying in the invariant subspace. This is a bubbling transition, since there is a switching between spatially homogeneous and nonhomogeneous states with statistical properties of on-off intermittency. Hence the onset of spatio-temporal chaos depends critically both on the existence of a chaotic attractor in the invariant subspace and its being transversely stable or unstable. (C) 2008 Elsevier B.V. All rights reserved.

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

Chaos rules : an exploration of the work of instructional designers in distance education

This thesis provides an examination of the work of instructional designers in distance education, through the conceptual lens of chaos theory. Chaos theory was chosen as an analytical tool because of its ability to reveal the patterns and processes of complex systems as they move between order and turbulence. Recent work in the social sciences, specifically literary theory, has provided impetus for applications of chaos theory to educational settings. Specifically, chaos theory is used to analyse eight case studies of projects volunteered by instructional designers working in five institutions in Hong Kong and Australia. Data were gathered over a period of months with each participant, chiefly through interviews, but also involving diary accounts, electronic mail and letters. The methodology was thus qualitative, specifically informed by Eisner's vision of the ‘critical connoisseur’. Eisner equates an ‘enlightened eye’ with attainment of the skills of a critical connoisseur. First, an effective qualitative researcher must develop connoisseurship, the art of appreciation. On its own, though, connoisseurship is not enough; it is a private act, and thus needs a public face or presence. Criticism is this link, criticism being the art of disclosure. The critical connoisseur aims to help others to increase perception and deepen understanding of an educational situation or event. In addition to the empirical work, a parallel strand of this thesis investigates the theory and reported practice of instructional design. A brief history of instructional design is presented, along with discussion of acknowledged deficiencies of current theory and approaches. Recent reported investigations of both theory and practice are analysed from the viewpoint of chaos theory. Examination of key contributions in the literature of instructional design and distance education reveals considerable resonance between these contributions and the fundamental properties of chaotic systems. Links are made, in both the theoretical and empirical strands, between instructional design and the behaviour of dissipative structures, attractors and the process of bifurcation. Use is also made of the time-dependent nature of chaos theory as a theory of becoming, rather than one of being. The thesis comprises eight chapters, two appendices and a references section. The introductory chapter explains the research problem, and outlines the structure of the thesis. Methodological considerations are left until after an assessment of instructional design literature and (reported) practice. This deliberately theoretical investigation (Chapters 2 and 3) comprises the first of the parallel strands that are presented. The basic conclusions are that instructional design theory has not been particularly helpful to or used by instructional designers, and that chaos theory might provide an alternative way of viewing instructional design practice. The other parallel strand is the empirical work, which for four chapters outlines the methodology and my findings concerning the role of instructional designers in distance education. The methodology is detailed in Chapter 4. Chapter 5 establishes the contexts of the participants, by examining their backgrounds and introductions to their roles. It also investigates their views on their role and status within their institutions and with working colleagues. Chapter 6 is an exploration of the major issues that influenced the work of the instructional designers. These are the issues that arose naturally in the interviews as the participants outlined the development and interactions that took place on a day to day basis. Time emerges as a key influence in their work, and its effects on the projects are outlined and analysed. The ways that instructional designers give advice to those with whom they work is also investigated. The next chapter continues consideration of their work, but this time as they reflect on their role and its demands. This includes their reactions to the various metaphors that have appeared in the literature, along with those that they introduced into our discussions. The links that are established between the two parallel strands are drawn more explicitly in the final chapter, Chapter 8, which is a notion of what a model of instructional design based on my conclusions might resemble. It summarises the evidence that it is not necessarily by striving for order—in fact quite the opposite — during key periods of course development, that leads to creative outcomes. The introduction of uncertainty and turbulence does, in some cases and under some conditions, move the system to a higher level. The image that is offered from chaos theory is that of time-bound dissipative structures, interacting with their open environment at far-from-equilibrium conditions, and transforming themselves from disorder to order through bifurcation. The role of strange or chaotic attractors is highlighted in the process. The first appendix gives background information in terms of the methodology. The second is the heart of the data upon which the thesis draws. That is, the second appendix outlines the case studies of the participants. Most are short summaries, but the final one is a detailed study, tracing the progress of the design and development of a subject in distance education.

Bifurcation analysis of a new Lorenz-like chaotic system

In this paper we study the local codimension one and two bifurcations which occur in a family of three-dimensional vector fields depending on three parameters. An equivalent family, depending on five parameters, was recently proposed as a new chaotic system with a Lorenz-like butterfly shaped attractor and was studied mainly from a numerical point of view, for particular values of the parameters, for which computational evidences of the chaotic attractor was shown. In order to contribute to the understand of this new system we present an analytical study and the bifurcation diagrams of an equivalent three parameter system, showing the qualitative changes in the dynamics of its solutions, for different values of the parameters. (C) 2007 Elsevier Ltd. All rights reserved.