Characterization of Stability Region for General Autonomous Nonlinear Dynamical Systems

The existing characterization of stability regions was developed under the assumption that limit sets on the stability boundary are exclusively composed of hyperbolic equilibrium points and closed orbits. The characterizations derived in this technical note are a generalization of existing results in the theory of stability regions. A characterization of the stability boundary of general autonomous nonlinear dynamical systems is developed under the assumption that limit sets on the stability boundary are composed of a countable number of disjoint and indecomposable components, which can be equilibrium points, closed orbits, quasi-periodic solutions and even chaotic invariant sets.

Representation of Neural Networks by Dynamical Systems

Representation of neural networks by dynamical systems is considered. The method of training of neural networks with the help of the theory of optimal control is offered.

Viability, Optimality and Stability of Dynamical Systems and Estimation of Convergence of Numerical Schemes

AMS subject classification: 49N35,49N55,65Lxx.

Critical Systems Theory: A Political Economy of Language, Thought, and Technology

An emergent form of political economy, facilitated by information and communication technologies (ICTs), is widely propagated as the apotheosis of unmitigated social, economic, and technological progress. Meanwhile, throughout the world, social degradation and economic inequality are increasing logarithmically. Valued categories of thought are, axiomatically, the basic commodities of the “knowledge economy”. Language is its means of exchange. This paper proposes a sociolinguistic method with which to critically engage the hyperbole of the “Information Age”. The method is grounded in a systemic social theory that synthesises aspects of autopoiesis and Marxist political economy. A trade policy statement is analysed to exemplify the sociolinguistically created aberrations that are today most often construed as social and political determinants.

Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.

Crowdsourcing information systems : a systems theory perspective

Crowdsourcing harnesses the potential of large and open networks of people. It is a relatively new phenomenon and attracted substantial interest in practice. Related research, however, lacks a theoretical foundation. We propose a system-theoretical perspective on crowdsourcing systems to address this gap and illustrate its applicability by using it to classify crowdsourcing systems. By deriving two principal dimensions from theory, we identify four fundamental types of crowdsourcing systems that help to distinguish important features of such systems. We analyse their respective characteristics and discuss implications and requirements for various aspects related to the design of such systems. Our results demonstrate that systems theory can inform the study of crowdsourcing systems. The identified system types and the implications on their design may prove useful for researchers to frame future studies and for practitioners to identify the right crowdsourcing systems for a particular purpose.

Different kinds of openings of Luhmann's systems theory: A reply to la Cour et al

Various researchers have called for an 'opening up' of Luhmann's systems theory. We take this short paper as an occasion for a critical reflection on the necessity, existence and possibilities of such an opening. We start by pointing out the inherent openness of Luhmann's theory, and, based on this, discuss three kinds of openings: the international opening, the theoretical opening and the empirical opening. With regard to the latter, we distinguish three general options of using Luhmann's theory for empirical research. Copyright © 2007 SAGE.

Analyses of systems theory for construction accident prevention with specific reference to OSHA accident reports

To enhance workplace safety in the construction industry it is important to understand interrelationships among safety risk factors associated with construction accidents. This study incorporates the systems theory into Heinrich’s domino theory to explore the interrelationships of risks and break the chain of accident causation. Through both empirical and statistical analyses of 9,358 accidents which occurred in the U.S. construction industry between 2002 and 2011, the study investigates relationships between accidents and injury elements (e.g., injury type, part of body, injury severity) and the nature of construction injuries by accident type. The study then discusses relationships between accidents and risks, including worker behavior, injury source, and environmental condition, and identifies key risk factors and risk combinations causing accidents. The research outcomes will assist safety managers to prioritize risks according to the likelihood of accident occurrence and injury characteristics, and pay more attention to balancing significant risk relationships to prevent accidents and achieve safer working environments.

Learning processes in creative service teams : towards a dynamic systems theory

The fastest-growing segment of jobs in the creative sector are in those firms that provide creative services to other sectors (Hearn, Goldsmith, Bridgstock, Rodgers 2014, this volume; Cunningham 2014, this volume). There are also a large number of Creative Services (Architecture and Design, Advertising and Marketing, Software and Digital Content occupations) workers embedded in organizations in other industry sectors (Cunningham and Higgs 2009). Ben Goldsmith (2014, this volume) shows, for example, that the Financial Services sector is the largest employer of digital creative talent in Australia. But why should this be? We argue it is because ‘knowledge-based intangibles are increasingly the source of value creation and hence of sustainable competitive advantage (Mudambi 2008, 186). This value creation occurs primarily at the research and development (R and D) and the marketing ends of the supply chain. Both of these areas require strong creative capabilities in order to design for, and to persuade, consumers. It is no surprise that Jess Rodgers (2014, this volume), in a study of Australia’s Manufacturing sector, found designers and advertising and marketing occupations to be the most numerous creative occupations. Greg Hearn and Ruth Bridgstock (2013, forthcoming) suggest ‘the creative heart of the creative economy […] is the social and organisational routines that manage the generation of cultural novelty, both tacit and codified, internal and external, and [cultural novelty’s] combination with other knowledges […] produce and capture value’. 2 Moreover, the main “social and organisational routine” is usually a team (for example, Grabher 2002; 2004).

Electromechanical wave in power systems : theory and applications

The continuum model is a key paradigm describing the behavior of electromechanical transients in power systems. In the past two decades, much research work has been done on applying the continuum model to analyze the electromechanical wave in power systems. In this work, the uniform and non-uniform continuum models are first briefly described, and some explanations borrowing concepts and tools from other fields are given. Then, the existing approaches of investigating the resulting wave equations are summarized. An application named the zero reflection controller based on the idea of the wave equations is next presented.

Career Development and Systems Theory : Connecting Theory and Practice [3rd edition]

"The 3rd edition of this classic book offers practitioners, researchers and students a comprehensive introduction to, and overview of, career theory; introduces the Systems Theory Framework of career development; and demonstrates its considerable contemporary and innovative application to practice. A number of authors have identified the framework as one of a small number of significant innovations in the career development literature. The Systems Theory Framework of career development was developed to provide coherence to the career development field by providing a comprehensive conceptualisation of the many existing theories and concepts relevant to understanding career development. It is not designed to be a theory of career development; rather systems theory is introduced as the basis for an overarching, or metatheoretical, framework within which all concepts of career development, described in the plethora of career theories, can be usefully positioned and utilised in both theory and practice. It has been applied to the career development of children, adolescents and women. Since its first publication, the Systems Theory Framework has been the basis of numerous publications focusing on theoretical application and integration, practice and research, with a growing number of these by authors other than the framework developers. Its application across cultures also has been emphasised. The theoretical and practical unity of the Systems Theory Framework makes this book a worthy addition to the professional libraries of practitioners, researchers and students, new to, or experienced in, the field of career development."--PUBLISHER WEBSITE

A contextualised general systems theory

A system is something that can be separated from its surrounds, but this definition leaves much scope for refinement. Starting with the notion of measurement, we explore increasingly contextual system behaviour, and identify three major forms of contextuality that might be exhibited by a system: (a) between components; (b) between system and experimental method, and; (c) between a system and its environment. Quantum Theory is shown to provide a highly useful formalism from which all three forms of contextuality can be analysed, offering numerous tests for contextual behaviour, as well as modelling possibilities for systems that do indeed display it. I conclude with the introduction of a Contextualised General Systems Theory based upon an extension of this formalism.