Study of Singularities in Nonsmooth Dynamical Systems via Singular Perturbation

In this article we describe some qualitative and geometric aspects of nonsmooth dynamical systems theory around typical singularities. We also establish an interaction between nonsmooth systems and geometric singular perturbation theory. Such systems are represented by discontinuous vector fields on R(l), l >= 2, where their discontinuity set is a codimension one algebraic variety. By means of a regularization process proceeded by a blow-up technique we are able to bring about some results that bridge the space between discontinuous systems and singularly perturbed smooth systems. We also present an analysis of a subclass of discontinuous vector fields that present transient behavior in the 2-dimensional case, and we dedicate a section to providing sufficient conditions in order for our systems to have local asymptotic stability.

Local dimension and finite time prediction in spatiotemporal chaotic systems

Predictability is related to the uncertainty in the outcome of future events during the evolution of the state of a system. The cluster weighted modeling (CWM) is interpreted as a tool to detect such an uncertainty and used it in spatially distributed systems. As such, the simple prediction algorithm in conjunction with the CWM forms a powerful set of methods to relate predictability and dimension.

Management of vomplex systems: Modeling the biological pest control

The aim of this paper is to study the cropping system as complex one, applying methods from theory of dynamic systems and from the control theory to the mathematical modeling of the biological pest control. The complex system can be described by different mathematical models. Based on three models of the pest control, the various scenarios have been simulated in order to obtain the pest control strategy only through natural enemies' introduction. © 2008 World Scientific Publishing Company.

Generic bifurcation of refracted systems

In this article we discuss some qualitative and geometric aspects of non-smooth dynamical systems theory. Our goal is to study the diagram bifurcation of typical singularities that occur generically in one parameter families of certain piecewise smooth vector fields named Refracted Systems. Such systems has a codimension-one submanifold as its discontinuity set. © 2012 Elsevier Ltd.

Discrete Event Systems based Design Patterns for Diagnosability Analysis of Automated Manufacturing Systems

The main goal of this thesis is to facilitate the process of industrial automated systems development applying formal methods to ensure the reliability of systems. A new formulation of distributed diagnosability problem in terms of Discrete Event Systems theory and automata framework is presented, which is then used to enforce the desired property of the system, rather then just verifying it. This approach tackles the state explosion problem with modeling patterns and new algorithms, aimed for verification of diagnosability property in the context of the distributed diagnosability problem. The concepts are validated with a newly developed software tool.

Risk Judgment in Obsessive-Compulsive Disorder: Testing a Dual-Systems Account

Dual-systems theorists posit distinct modes of reasoning. The intuition system reasons automatically and its processes are unavailable to conscious introspection. The deliberation system reasons effortfully while its processes recruit working memory. The current paper extends the application of such theories to the study of Obsessive-Compulsive Disorder (OCD). Patients with OCD often retain insight into their irrationality, implying dissociable systems of thought: intuition produces obsessions and fears that deliberation observes and attempts (vainly) to inhibit. To test the notion that dual-systems theory can adequately describe OCD, we obtained speeded and unspeeded risk judgments from OCD patients and non-anxious controls in order to quantify the differential effects of intuitive and deliberative reasoning. As predicted, patients deemed negative events to be more likely than controls. Patients also took more time in producing judgments than controls. Furthermore, when forced to respond quickly patients' judgments were more affected than controls'. Although patients did attenuate judgments when given additional time, their estimates never reached the levels of controls'. We infer from these data that patients have genuine difficulty inhibiting their intuitive cognitive system. Our dual-systems perspective is compatible with current theories of the disorder. Similar behavioral tests may prove helpful in better understanding related anxiety disorders. (C) 2013 Elsevier Ltd. All rights reserved.

Control and command systems concepts from early work on a Mars Rover

We recover and develop some robotic systems concepts (on the light of present systems tools) that were originated for an intended Mars Rover in the sixties of the last century at the Instrumentation Laboratory of MIT, where one of the authors was involved. The basic concepts came from the specifications for a type of generalized robot inspired in the structure of the vertebrate nervous systems, where the decision system was based in the structure and function of the Reticular Formation (RF). The vertebrate RF is supposed to commit the whole organism to one among various modes of behavior, so taking the decisions about the present overall task. That is, it is a kind of control and command system. In this concepts updating, the basic idea is that the RF comprises a set of computing units such that each computing module receives information only from a reduced part of the overall, little processed sensory inputs. Each computing unit is capable of both general diagnostics about overall input situations and of specialized diagnostics according to the values of a concrete subset of the input lines. Slave systems to this command and control computer, there are the sensors, the representations of external environment, structures for modeling and planning and finally, the effectors acting in the external world.

Ontological evaluation of enterprise systems interoperability using ebXML

Enterprise systems interoperability (ESI) is an important topic for business currently. This situation is evidenced, at least in part, by the number and extent of potential candidate protocols for such process interoperation, viz., ebXML, BPML, BPEL, and WSCI. Wide-ranging support for each of these candidate standards already exists. However, despite broad acceptance, a sound theoretical evaluation of these approaches has not yet been provided. We use the Bunge-Wand-Weber (BWW) models, in particular, the representation model, to provide the basis for such a theoretical evaluation. We, and other researchers, have shown the usefulness of the representation model for analyzing, evaluating, and engineering techniques in the areas of traditional and structured systems analysis, object-oriented modeling, and process modeling. In this work, we address the question, what are the potential semantic weaknesses of using ebXML alone for process interoperation between enterprise systems? We find that users will lack important implementation information because of representational deficiencies; due to ontological redundancy, the complexity of the specification is unnecessarily increased; and, users of the specification will have to bring in extra-model knowledge to understand constructs in the specification due to instances of ontological excess.

Strategic development process and complex adaptive systems

The two areas of theory upon which this research was based were „strategy development process?(SDP) and „complex adaptive systems? (CAS), as part of complexity theory, focused on human social organisations. The literature reviewed showed that there is a paucity of empirical work and theory in the overlap of the two areas, providing an opportunity for contributions to knowledge in each area of theory, and for practitioners. An inductive approach was adopted for this research, in an effort to discover new insights to the focus area of study. It was undertaken from within an interpretivist paradigm, and based on a novel conceptual framework. The organisationally intimate nature of the research topic, and the researcher?s circumstances required a research design that was both in-depth and long term. The result was a single, exploratory, case study, which included use of data from 44 in-depth, semi-structured interviews, from 36 people, involving all the top management team members and significant other staff members; observations, rumour and grapevine (ORG) data; and archive data, over a 5½ year period (2005 – 2010). Findings confirm the validity of the conceptual framework, and that complex adaptive systems theory has potential to extend strategy development process theory. It has shown how and why the strategy process developed in the case study organisation by providing deeper insights to the behaviour of the people, their backgrounds, and interactions. Broad predictions of the „latent strategy development? process and some elements of the strategy content are also possible. Based on this research, it is possible to extend the utility of the SDP model by including peoples? behavioural characteristics within the organisation, via complex adaptive systems theory. Further research is recommended to test limits of the application of the conceptual framework and improve its efficacy with more organisations across a variety of sectors.

Synchronization processes in nonlinear systems and their relation to cortical oscillatory dynamics

This thesis was focused on theoretical models of synchronization to cortical dynamics as measured by magnetoencephalography (MEG). Dynamical systems theory was used in both identifying relevant variables for brain coordination and also in devising methods for their quantification. We presented a method for studying interactions of linear and chaotic neuronal sources using MEG beamforming techniques. We showed that such sources can be accurately reconstructed in terms of their location, temporal dynamics and possible interactions. Synchronization in low-dimensional nonlinear systems was studied to explore specific correlates of functional integration and segregation. In the case of interacting dissimilar systems, relevant coordination phenomena involved generalized and phase synchronization, which were often intermittent. Spatially-extended systems were then studied. For locally-coupled dissimilar systems, as in the case of cortical columns, clustering behaviour occurred. Synchronized clusters emerged at different frequencies and their boundaries were marked through oscillation death. The macroscopic mean field revealed sharp spectral peaks at the frequencies of the clusters and broader spectral drops at their boundaries. These results question existing models of Event Related Synchronization and Desynchronization. We re-examined the concept of the steady-state evoked response following an AM stimulus. We showed that very little variability in the AM following response could be accounted by system noise. We presented a methodology for detecting local and global nonlinear interactions from MEG data in order to account for residual variability. We found crosshemispheric nonlinear interactions of ongoing cortical rhythms concurrent with the stimulus and interactions of these rhythms with the following AM responses. Finally, we hypothesized that holistic spatial stimuli would be accompanied by the emergence of clusters in primary visual cortex resulting in frequency-specific MEG oscillations. Indeed, we found different frequency distributions in induced gamma oscillations for different spatial stimuli, which was suggestive of temporal coding of these spatial stimuli. Further, we addressed the bursting character of these oscillations, which was suggestive of intermittent nonlinear dynamics. However, we did not observe the characteristic-3/2 power-law scaling in the distribution of interburst intervals. Further, this distribution was only seldom significantly different to the one obtained in surrogate data, where nonlinear structure was destroyed. In conclusion, the work presented in this thesis suggests that advances in dynamical systems theory in conjunction with developments in magnetoencephalography may facilitate a mapping between levels of description int he brain. this may potentially represent a major advancement in neuroscience.

Integrated manufacturing systems design in a multi-product company

Using a hydraulic equipment manufacturing plant as the case study, this work explores the problems of systems integration in manufacturing systems design, stressing the behavioural aspects of motivation and participation, and the constraints involved in the proper consideration of the human sub-system. The need for a simple manageable modular organisation structure is illustrated, where it is shown, by reference to systems theory, how a business can be split into semi-autonomous operating units. The theme is the development of a manufacturing system based on an analysis of the business, its market, product, technology and constraints, coupled with a critical survey of modern management literature to develop an integrated systems design to suit a specific company in the current social environment. Society currently moves through a socio-technical revolution with man seeking higher levels of motivation. The transitory environment from an autocratic/paternalistic to a participative operating mode demands systems parameters only found to a limited extent in manufacturing systems today. It is claimed, that modern manufacturing systems design needs to be based on group working, job enrichment, delegation of decision making and reduced job monotony. The analysis shows how negative aspects of cellular manufacture such as lack of flexibility and poor fixed asset utilisation are relatively irrelevant and misleading in the broader context of the need to come to terms with the social stresses imposed on a company operating in the industrial environment of the present and the immediate future.