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In this paper, we present a brief study on various paradigms to tackle complexity or in other words manage uncertainty in the context of understanding science, society and nature. Fuzzy real numbers, fuzzy logic, possibility theory, probability theory, Dempster‐Shafer theory, artificial neural nets, neuro‐fuzzy, fractals and multifractals, etc. are some of the paradigms to help us to understand complex systems. We present a very detailed discussion on the mathematical theory of fuzzy dynamical system (FDS), which is the most fundamental theory from the point of view of evolution of any fuzzy system. We have made considerable extension of FDS in this paper, which has great practical value in studying some of the very complex systems in society and nature. The theories of fuzzy controllers, fuzzy pattern recognition and fuzzy computer vision are but some of the most prominent subclasses of FDS. We enunciate the concept of fuzzy differential inclusion (not equation) and fuzzy attractor. We attempt to present this theoretical framework to give an interpretation of cyclogenesis in atmospheric cybernetics as a case study. We also have presented a Dempster‐Shafer's evidence theoretic analysis and a classical probability theoretic analysis (from general system theoretic outlook) of carcinogenesis as other interesting case studies of bio‐cybernetics.

Consumers are inclined to join longer queues due to social interactions in service consumptions. This purchase behavior brings in operational challenges in terms of capacity planning, which affects consumers’ demand, leading to an unstable and fluctuated arrival process. This paper aims to investigate the dynamic characteristics of the arrival process of a service system with boundedly rational consumers whose purchase decisions are influenced by the queue length under social interactions.

Consumers’ bounded rationality is modeled based on the random utility theory. Due to social interactions, the equilibrium queue length and its interaction with the expected waiting time affect consumers’ value perception. The authors first analyze the optimal service capacity decision with or without considering the influence of social interactions in a static setting. They then focus on the dynamic characteristics of the arrival process by a one-dimensional dynamical model in terms of the arrival rate.

This paper finds that the service system can behave chaotic in terms of arrival rate dynamics under social interactions. The results highlight the dynamical complexity of a simple service system due to consumers’ behavioral factors and the influence of social interactions, which may be the critical drivers leading to fluctuated and uneven demand.

The findings demonstrate that due to consumers’ limited cognitive ability and the influence of social interactions, the demand to a service system can be stable, periodic or even chaotic in terms of the arrival process. This study provides an alternative explanation to the observed demand fluctuations in various service processes under the influence of social interactions, which is important for service providers to effectively manage service capacity to achieve a stable service process and improve operational efficiency.

To develop a mathematical and algorithmic approach of avoiding the limitations of deterministically computing the values of energy, time, position and momentum imposed by Heisenberg's uncertainity principle (HUP) which is of profound significance from the point of view of some emerging science and technology like quantum computing, nano scale technology and chaotic dynamical systems.

A parametric method of establishing deterministic solutions for energy and momentum on the basis of quantized energy limits (instead of HUP) if developed in the non‐infinite non‐zero quantized energy limits where hidden deterministic solutions can be obtained for micro/nano structures.

The philosophical foundations of quantum mechanics as developed by Max Planck, Neils Bohrz, Werner Heisenburg, Dirac and Edwein Schrodinger is based on a duality concept of complimentarity notions. In most general logical sense for any physical reality qualitative dualism have to have a quantitative dualism may be hidden or virtual. The upper and lower limits of the dynamical quantum mechanical observables are determined based on the dimensional considerations for the physical constants H, C, G and H₀. The conceptual basis and mathematical framework of the paper in based Norbert Wiener's work on theory of cybernetics and D. Dutta Majumdars' unified cybernetic and general dynamical systems theory.

The testability of the theory needs to be established.

Without challenging HUP this is a contribution of tremendous practical implications.

It is often observed in practice that the essential behavior of mathematical models involving many variables can be captured by a much smaller model involving only a few variables. Further, the simpler model very often displays oscillatory behavior of some sort, especially when critical problem parameters are varied in certain ranges. This paper attempts to supply arguments from the theory of dynamical systems for why oscillatory behavior is so frequently observed and to show how such behavior emerges as a natural consequence of focusing attention upon so‐called “essential” variables in the process of model simplification. The relationship of model simplification and oscillatory behavior is shown to be inextricably intertwined with the problems of bifurcation and catastrophe in that the oscillations emerge when critical system parameters, i.e. those retained in the simple model, pass through critical regions. The importance of the simplification, oscillation and bifurcation pattern is demonstrated here by consideration of several examples from the environmental, economic and urban areas.

Surveys some of the important contributions of information theory (IT) to the understanding of systems science and cybernetics. Presents a short background on the main definitions of IT, and examines in which way IT could be thought of as a unified approach to general systems. Analyses the topics: syntax and semantics in information, information and self‐organization, entropy of forms (entropy of non‐random functions), and information in dynamical systems. Enumerates some suggestions for further research and takes this opportunity to describe new points of view, mainly by using entropy of non‐random functions.

Many international management scholars have expressed concern about whether societal culture changes so rapidly that research which attempts to represent it has little utility. We address this fundamental concern of international management by providing three theoretical lenses to examine the forces that produce and maintain a society's culture: functional theory, neo-institutional theory and complexity theory. We consider principles of progressive change and problems of social psychology from functional theory, the three pillars and conflicting institutional logics of neo-institutional theory and the ideas of stable equilibrium, oscillations and chaos of dynamic systems from complexity theory. Although these three theoretical lenses sometimes produce conflicting explanations of culture change, they often complement each other. Together, they provide a more realistic picture of the dynamics of the societal cultural milieu of organizations than do cultural representations that favour stability or those that completely discount the utility of any attempt at representing cultural continuity.

Online question-and-answer (Q&A) communities serve as important channels for knowledge diffusion. The purpose of this study is to investigate the dynamic development process of online knowledge systems and explore the final or progressive state of system development. By measuring the nonlinear characteristics of knowledge systems from the perspective of complexity science, the authors aim to enrich the perspective and method of the research on the dynamics of knowledge systems, and to deeply understand the behavior rules of knowledge systems.

The authors collected data from the programming-related Q&A site Stack Overflow for a ten-year period (2008–2017) and included 48,373 tags in the analyses. The number of tags is taken as the time series, the correlation dimension and the maximum Lyapunov index are used to examine the chaos of the system and the Volterra series multistep forecast method is used to predict the system state.

There are strange attractors in the system, the whole system is complex but bounded and its evolution is bound to approach a relatively stable range. Empirical analyses indicate that chaos exists in the process of knowledge sharing in this social labeling system, and the period of change over time is about one week.

This study contributes to revealing the evolutionary cycle of knowledge stock in online knowledge systems and further indicates how this dynamic evolution can help in the setting of platform mechanics and resource inputs.

To present an account of cognition integrating second‐order cybernetics (SOC) together with enactive perception and dynamic systems theory.

The paper presents a brief critique of classical models of cognition then outlines how integration of SOC, enactive perception and dynamic systems theory can overcome some weaknesses of the classical paradigm.

Presents the critique of evolutionary robotics showing how the issues of teleology and autonomy are left unresolved by this paradigm although their solution fits within the proposed framework.

The paper highlights the importance of genuine autonomy in the development of artificial cognitive systems. It sets out a framework within which the robotic research of cognitive systems could succeed.

There are no immediate practical implications but see research implications.

It joins the discussion on the fundamental nature of cognitive systems and emphasise the importance of autonomy and embodiment.

Proposes an application of fuzzy set theory to model epidemiological problems. Fuzzy logic has been revealed as a powerful predictive tool in the epidemiology of infectious diseases and some ideas are presented on how this could be done. This work presents an attempt to model the dynamics of rabies among a population of partially vaccinated dogs. This study demonstrates how a dynamical system can be modelled by fuzzy linguistic rules compared to the classical differential equations approach. The results are very encouraging and the approach through a more complex dynamical system is discussed in the final section.

The three-sector framework (relating to agriculture, manufacturing and services) is one of the major concepts for studying the long-run change of the economic structure. This paper aims to discuss the system-theoretical classification of the structural change in the three-sector framework and, in particular, its predictability by the Poincaré–Bendixson theory.

This study compares the assumptions of the Poincaré–Bendixson theory to the typical axioms of structural change modeling, the empirical evidence on the geometrical properties of structural change trajectories and the methodological arguments referring to the laws of structural change.

The findings support the assumption that the structural change phenomenon is representable by a dynamical system that is predictable by the Poincaré–Bendixson theory. This result implies, among others, that in the long run, structural change is either transitory or cyclical and can be used in further geometrical/topological long-run structural change modeling and prediction.

Although widespread in mathematics, geometrical/topological modeling methods have not been used in modeling and prediction of long-run structural change, despite the fact that they seem to be predestined for this purpose owing to their global, system-theoretical nature, allowing for a reduction of ideology content of predictions and greater robustness of results.