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This paper provides an introduction to three key concepts derived from chaos theory, with practical examples of each, which the authors believe can offer marketers an enriched understanding of the process by which they set out to construct an alternative future. A central tenet of chaos theory is that the future is inherently unpredictable in detail, but can be predicted in broad terms: what appears to be random (e.g. the unexpected results of a new marketing strategy) may turn out to be determined by a phenomenon known as an attractor. Marketing managers are setting out to “construct a future”. The broad outcomes of their actions may be predictable in general terms, but the path by which their organisations reach those outcomes, and the detailed stages through which they pass, are not – however sound their conventional marketing planning may be. Practising marketing managers may understandably have reservations about transferring concepts which have not yet been fully tested in the natural sciences, where they have their origin, into marketing planning. Nevertheless, many are not in fact unique to chaos theory. Therefore, they are used here as a metaphor, to encourage managers to take a different view of the strategic issues facing their organisations, and to question the conventional wisdom that executive action can be taken on the basis of extensive rational analysis, in the expectation that it will achieve predetermined objectives. This paper thereby offers novel insights into the process of redefining markets and the opportunities that they provide. The attractor metaphor holds out a number of challenges for innovative marketers, as well as some cautionary lessons.

Fractional calculus provides powerful tool to build more realistic and accurate mathematical models in economic field. This paper aims to explore a proposed fractional-order differentiated Cournot duopoly game and its discretized game.

Conditions for existence and uniqueness of the proposed game’s solution are derived. The existence of Nash equilibrium point and its local and global stability are obtained. Furthermore, local stability analysis of the discretized game is investigated. The effects of fractional-order on game’s dynamics are examined, along with other parameters of the game, via the 2D bifurcation diagrams in planes of system’s parameters are acquired.

Theoretical and numerical simulation results demonstrate rich variety of interesting dynamical behaviors such as period-doubling and Neimark–Sacker bifurcations, attractors’ crises in addition to chaotic attractors. The results demonstrated that the stability Nash equilibrium point of the game can be lost by period doubling or Neimark–Sacker bifurcations.

Oligopoly games are pivotal in the mathematical modeling of some substantial economic areas such as industrial organization, airline, banking, telecommunication companies, international trade and also macroeconomic analysis of business cycles, innovation and growth.

Although the Cournot game and its variants have attracted great interest among mathematicians and economists since the time of its proposition till present, memory effects in continuous-time and discrete-time Cournot duopoly game have not been addressed yet. To the best of author’s knowledge, this can be considered as the first attempt to investigate this problem of fractional-order differentiated Cournot duopoly game. In addition, studying more realistic models of Cournot oligopoly games plays a pivotal role in the mathematical investigation and better understanding of some substantial economic areas such as industrial organization, airline, banking, telecommunication companies, international trade and also in macroeconomic analysis of business cycles, innovation and growth.

Industries lament the current situation of approaches that have resulted in huge losses in the face of complex risks. The purpose of this study is therefore to review complexity theory in the context of risk management so that it is possible to research better approaches for managing complex risks.

The approach is to review complexity theory and highlight those aspects of complexity theory that have relevance for risk management. Then, the paper ends with a discussion on what direction of research that will be most promising for the aforementioned purpose.

The paper finds that the most challenging aspect is to identify the weak signals, and this implies that the current approaches of estimating probabilities are not going to produce the desired results. Big data may hold a solution in the future, but with legislation such as the General Data Protection Regulation, this seems impossible to implement on ethical grounds. Hence, the most prudent approach is to use a margin of safety as advocated by Graham roughly 70 years ago. Indeed, the approach may be to assume that a disaster will take place and use risk management tools to estimate the impact for a given object.

The literature review is a summary of a much larger work, and in so doing, the resulting simplification may run the risk of missing out on important details. However, with this risk in mind, the review holds rich enough discussion on complexity to be relevant for research about complex risk management.

The current implication for practice is that the paper strongly supports the notion of using a margin of safety as advocated by Graham and his most famous disciple Warren Buffet. This comes from the fact that because context is king, risk management approaches must be applied in their right domain. There is no one right way. In the future, the goal is to develop a quantitative approach that can help the industry in pricing complex risks.

The main contribution of the paper is to bring complexity theory more into the domain of risk management with sufficient details that should allow researchers to get conceptual ideas about what might work or not concerning complex risk management. If nothing else, it would be a significant contribution of the paper if it could help increasing the interest in complexity theory.

Addresses the lack of success in educational reform efforts by utilizing a metacognitive analysis of the base assumption of most, if not all, current reform efforts. Suggests a different theoretical orientation and perspective for understanding education and attempts to improve it. By contrasting the common orientation of today and the one proposed, the paper applies this new perspective to two examples. Examines educational reform in light of the orientation proposed.

The purpose of this paper is to open up the question of how we prepare people to be resilient, flexible and capable of managing the uncertainties and complexities of the twenty‐first century by using both futures studies and complexity theory as a backdrop for a discussion of career education and teacher education in the future.

Recent developments in the work of others in futures studies and complexity theory are presented. These developments provide a framework for discussing current understandings of career and teacher education and to explore the possible trajectories for supporting learning to, in and through work across the lifespan.

Through applying futures studies and complexity theory to career and teacher education the authors conclude that these conceptual frameworks have much to offer practitioners and policy makers in the fields of career education and teacher education, and that theory development in these fields is already embracing the conceptual tools within these areas of study.

Suggestions are made for what will be needed in the future and how educational organisations will have to adapt in order to promote resilience and flexibility in the face of the uncertainty and complexity of learning and work in the twenty‐first century.

This paper brings together four distinct areas of research and scholarship – i.e. complexity theory, futures studies, career and teacher education – in order to explore possible and desirable trajectories for supporting learning to, in and through work across the lifespan.

The information age has highlighted the complex nature of our organizing systems. Complex systems move between ordered and disordered states. Ordered states condense near attractor points which include bifurcation points where order is redefined for the system. Such points have occurred repeatedly in our economy over the past decade, causing an unpredictable environment. As our economy moves from a stable state, a different set of organizing rules is needed. When this new set of organizing rules are overlaid with the conditions and processes facilitated by the use of advanced communication and computing technology, we find that virtual or network organizations are an emerging logical form for organizing.

The purpose of this study is to analyze the corrosion behavior of 304SS in three kinds of solution, 3.5 per cent NaCl, 5 per cent H₂SO₄ and 1 M (1 mol/L) NaOH, using electrochemical noise.

Corrosion types and rates were characterized by spectrum and time-domain analysis. EN signals were evaluated using a novel method of phase space reconstruction and chaos theory. To evaluate the chaotic characteristics of corrosion systems, the delay time was obtained by the mutual information method and the embedding dimension was obtained by the average false neighbors method.

The varying degrees of chaos in the corrosion systems were indicated by positive largest Lyapunov exponents of the electrochemical potential noise.

The change of correlation dimension in three kinds of solution demonstrated significant differences, clearly differentiating various types of corrosion.

The traditional management skills of planning, organizing, directing and controlling are inadequate in the fast‐paced, constantly changing, highly complex world of twenty‐first century organizations. This article uses concepts from quantum mechanics and chaos theory as metaphors for a new management skill set that can enable managers to actualize more of their leadership potential. The seven quantum skills are ancient and futuristic, scientific and spiritual, simple and complex. Together they form a model that balances the traditional left‐brain management skills with new skills that more fully utilize both hemispheres of the brain. As managers master these skills, they transcend the limitations of mechanistic, deterministic, reductionistic thinking and become authentic change masters, changing themselves and their organizations at depth.

Cost overrun is inherent to project chaos, which is one of the key drivers of project failure. The purpose of this paper is to explore the critical elements of complexity-risk interdependency for cost-chaos in the construction management domain by utilizing a multi-criteria decision model.

A total of 12 complexity and 60 risk attributes are initially identified from the literature and using expert’s judgements. For the development of a structured hierarchy of key complexity and risk drivers, a real-time Delphi process is adopted for recording and evaluating the responses from experts. Afterwards, a pair-wise comparison using analytical network processing is performed to measure complexity-risk interdependencies against cost alternatives.

The findings of the integrated priority decision index (IPDI) suggest that uncertainties related to contingency and escalation costs are the main sources of cost overrun in project drift, along with the key elements such as “the use of innovative technology,” “multiple contracts,” “low advance payment,” “change in design,” “unclear specifications” and “the lack of experience” appear to be more significant to chaos in complexity-risk interdependency network.

This study did not address the uncertainty and vulnerability exit in the judgment process, therefore, this framework can be extended using fuzzy logic to better evaluate the significance of cost-chaos drivers.

These results may assist the management of cost overrun to avoid chaos in a project. The proposed model can be applied within project risk management practices to make better-informed technical decisions in the early phases of the project life cycle where uncertainty is high.

This research addresses the importance of cost overruns as a source of project chaos in dynamic systems where projects reach the edge of chaos and progress stops. A new IPDI index contributes toward evaluating the severity of complexity and risk and their interdependencies which create cost-chaos in infrastructure transport projects.

This paper considers supply chain management organizations with the aid of 'chaotic systems theory' developed originally in physics and mathematics. Since innovations in supply chain management are vital for organizational survival 'complex systems theory' may assist in fine-tuning managerial philosophies that provide stability in supply chain management because it is on the boundary of chaos that the greatest innovational creativity occurs. Neither 'management by rigid objectives' (MBO) nor 'management by instruction' (MBI) will be suitable for the information society of the twenty-first century because chaotic social systems will no longer be effectively managed. However, the capacity for self-organization will be derived essentially from how supply chain management members accept a shared set of values or principles for action-'management by values' (MBV). Complex systems theory deals with systems that show complex structures in time or space, often hiding simple deterministic rules. This theory holds that once these rules are found, it is possible to make effective predictions and even to control the apparent complexity. The state of chaos that self-organizes is attributable to the appearance of the 'strange attractor' and provides the ideal basis for creativity and innovation in the twenty-first century. In the self-organized state of chaos, social members are not confined to narrow roles and gradually develop their capacity for differentiation and relationships, growing progressively towards their maximum potential contribution to the efficiency of the organization. In this meaning, values act as organizers of 'attractors' of disorder, which, in the theory of chaos, are systems represented by usually regular geometric configurations that predict the long-term behavior of complex systems. In supply chain management organizations (as in all kinds of social systems) the initial principles end up as the final principles in the long term. An attractor is a model representation of the behavioral results of the system. The attractor is not a force of attraction or a goal-oriented presence in the system; it simply depicts where the system is heading based on its rules of motion. In supply chain management organizations that cultivate or shares values of autonomy, responsibility, independence, innovation, creativity, and proactivity, the risk of short-term chaos is mitigated by external complexities that organizations are currently confronting. The strategy is to alter the supply chain management's surroundings so that they can benefit from management by values (MBV).