Homoclinic bifurcations in reversible systems

Zusammenfassung zur Dissertation: Homoclinic Bifurcations in Reversible Systems von Thomas Wagenknecht eingereicht bei der Fakultät für Mathematik und Naturwissenschaften der Technischen Universität Ilmenau am 17. Juni 2003 öffentlich verteidigt am 12. Dezember 2003 Gutachter: Prof. Dr. A. R. Champneys (University of Bristol) Prof. Dr. B. Fiedler (Freie Universität Berlin) Prof. Dr. B. Marx (Technische Universität Ilmenau) Zusammenfassung Die vorliegende Arbeit untersucht Bifurkationen homokliner Lösungen in gewöhnlichen Differentialgleichungen. Homokline Lösungen sind in positiver und negativer Zeit asymptotisch zu einer Gleichgewichtslage, d.h. zu einer konstanten Lösung der Differentialgleichung. Die Arbeit betrachtet solche homokline Bifurkationen, die von einer Veränderung des Typs dieser assoziierten Gleichgewichtslage herrühren. Verschiedene Szenarien werden in der Klasse der reversiblen Differentialgleichungen analysiert. Der Hauptteil der Arbeit beschäftigt sich mit Homoklinen an Gleichgewichtslagen, welche selbst in einer lokalen Bifurkation verzweigen. Dabei verändert sich der Typ der Gleichgewichtslage vom reellen Sattel (mit führenden reellen Eigenwerten) zum Sattel-Zentrum (mit einem Paar rein imaginärer Eigenwerte). Das Miteinander lokaler und globaler Bifurkationseffekte erfordert eine neuartige Behandlung: Durch eine Kombination analytischer und geometrischer Techniken wird eine Beschreibung verzweigender Homoklinen gewonnen. Dabei werden sowohl rein reversible Systeme als auch Systeme mit zusätzlicher Symmetrie und Hamilton-Struktur betrachtet. Im zweiten Teil der Arbeit werden homokline Bifurkationsphänomene untersucht, die von einer Typveränderung der Gleichgewichtslage von rellem Sattel zu komplexem Sattel- Fokus (mit komplexen führenden Eigenwerten) herrühren. Dabei wird die Existenz von zwei Ausgangshomoklinen in sogenannter Blasebalg-Konfiguration (homoclinic bellows configuration) vorausgesetzt. Unter Verwendung einer auf Lin zurückgehenden analytischen Methode werden Bifurkationsresultate für verzweigende N-Homoklinen erzielt. Die allgemeinen Bifurkationsresultate werden auf physikalische Probleme der nichtlinearen Optik und Wasserwellentheorie, sowie auf zwei mathematische Modellgleichungen angewendet und in numerischen Untersuchungen bestätigt.The thesis investigates bifurcations from homoclinic solutions of ordinary differential equations. Homoclinic solutions are characterised by approaching an equilibrium, i.e. a constant solution of a differential equation, in both positive and negative time. The thesis is devoted to the analysis of homoclinic bifurcations that originate from a change in the type of the associated equilibrium. Several scenarios are considered in the class of reversible ordinary differential equations. The main part of the thesis deals with solutions homoclinic to equilibria that themselves undergo a local bifurcation. In this process the type of the equilibrium changes from a real saddle (with real leading eigenvalues) to a saddle-centre (with a pair of imaginary eigenvalues). The interplay of local and global bifurcation effects requires a new analytical approach. By a combination of analytical and geometric techniques a description of bifurcating homoclinic solutions is derived. Thereby both purely reversible systems and systems with additional symmetry or Hamiltonian structure are considered. The second part of the thesis discusses a homoclinic bifurcation in which the associated equilibrium undergoes a transition from real saddle to complex saddle-focus (with complex leading eigenvalues). The existence of two primary homoclinic solutions forming a so-called bellows structure is assumed. Using an analytical technique known as Lin?s method results about the bifurcation of N-homoclinic orbits are derived. The theory is applied to physical problems from nonlinear optics and water wave theory as well as to two mathematical model systems. Numerical investigations confirm the general bifurcation results

Waking Up a Sleeping Giant: Lessons from Two Extended Pilots to Transform Public Organizations by Internal Crowdsourcing

Digital transformation is a main driver for change, evolution, and disruption in organizations. As digital transformation is not solely determined by technological advancements, public environments necessitate changes in organizational practice and culture alike. A mechanism that seeks to realize employee engagement to adopt innovative modes of problem-solving is internal crowdsourcing, which flips the mode of operation from top-down to bottom-up. This concept is thus disrupting public organizations, as it heavily builds on IT-enabled engagement platforms that overcome the barriers of functional expertise and routine processes. Within this paper, we reflect on two design science projects that were piloted for six months within public organizations. We derive insights on the sociotechnical effects of internal crowdsourcing on organizational culture, social control, individual resources, motivation, and empowerment. Furthermore, using social cognitive theory, we propose design propositions for internal crowdsourcing, that guide future research and practice-oriented approaches to enable innovation in public organizations

Crowdsourcing in a Public Organization: Transformation and Culture

Employees increasingly want to participate in the decision-making processes of their organization. Approaches that facilitate organizational participation, such as internal crowdsourcing platforms, can achieve this. However, although organizations of various backgrounds should be able to reap benefits from such systems, in practice, implementation might fail due to an organizational culture built on hierarchical structures, low experience with employee participation and fixed processes. Taking a design science approach, we explore this relation in a five-month case study of a transformational process at a public organization. We design, implement and evaluate an information system for internal crowdsourcing. Based on the results from user-generated content analysis of the proposals and comments, survey data and several in-depth interviews, we observe an IT culture conflict that significantly affects system adoption and use. Our findings contribute to the discussion on theoretical and practical implications for design and implementation of information systems in organizational contexts

PEER RATINGS AND ASSESSMENT QUALITY IN CROWD-BASED INNOVATION PROCESSES

Social networks – whether public or in enterprises – regularly ask users to rate their peers’ content using different voting techniques. When employed in innovation challenges, these rating procedures are part of an open, interactive, and continuous engagement among customers, employees, or citizens. In this regard, assessment accuracy (i.e., correctly identifying good and bad ideas) in crowdsourced eval-uation processes may be influenced by the display of peer ratings. While it could sometimes be useful for users to follow their peers, it is not entirely clear under which circumstances this actually holds true. Thus, in this research-in-progress article, we propose a study design to systematically investigate the effect of peer ratings on assessment accuracy in crowdsourced idea evaluation processes. Based on the elaboration likelihood model and social psychology, we develop a research model that incorporates the mediating factors extraversion, locus of control, as well as peer rating quality (i.e., the ratings’ corre-lation with the evaluated content’s actual quality). We suggest that the availability of peer ratings de-creases assessment accuracy and that rating quality, extraversion, as well as an internal locus of control mitigate this effect

Unhelpful, caustic and slow: the academic community should rethink the way publications are reviewed

The current review system for many academic articles is flawed, hindering the publication of excellent, timely research. There is a lack of education for peer reviewers, either during PhD programmes or from journal publishers, and the lack of incentives to review compounds the problem. Thomas Wagenknecht offers up some solutions to the current system, including encouraging associate editors to use their authority to mitigate the impact of bad reviewers, shortening the entire peer review process, and increasing peer reviewer education during PhD and even Masters programmes. However, there are also opportunities for more significant reforms, by adopting post-publication peer review and by exploiting new distributed ledger technologies

Organizational Online Participation

As today’s employees demand higher degrees of involvement in terms of how, when, and where they work, open innovation and (internal) crowdsourcing are being widely adopted. Despite recent efforts by many organizations to implement such systems in order to increase the possibilities for organizational participation, studies have only narrowly explored how their design affects employee opinions and communication as well as how organizational culture influences usage and adoption. This thesis investigates the conditions, capabilities and components for the design of organizational online participation systems, applying a Design Science Research approach. Following a literature review on idea generation, collaboration and evaluation in open innovation processes, we outline success factors for open innovation systems. We validate our success factors in practice by conducting semi-structured interviews with 20 experts from mid- and large-cap private and public organizations in Germany. Moreover, we derive three key challenges that guide our subsequent studies. First, we investigate the “Bag of Lemons” approach, a novel rating technique, and compare it to the standard techniques Likert scales and up- and down-voting. Our study with 141 participants in an open innovation engagement at a public-private research organization finds that BOL is perceived as more frustrating than the other two rating techniques, which is partly mediated by the significantly increased information overload. Second, we turn to anonymity in two distinct studies. We analyze the effect of anonymity, as compared to identifiability of user profiles, on communication persuasiveness – operationalized as actual opinion change – in a two-staged online experimental survey with 377 participants. We find anonymity to be a double-edged sword as it decreases perceived social presence, which in turn affects both user involvement as well as perceived user credibility. Thereafter, we investigate the design of a feature for optional anonymous contributions and its effect on participation and the choice of language in an internal crowdsourcing platform. Our analysis of an implementation and five-month test at a public organization with more than 110 employees shows the effectiveness of our “opt-in anonymity” feature as we elicit participation from otherwise reticent employees and no disinhibited language. Third, we analyze the design of an internal crowdsourcing system at this public organization in more detail, focusing on the influence of its organizational culture on usage and acceptance. We assert an IT-culture-conflict, as the organizational values do not match the open and communal approach transposed by the crowdsourcing system. We suggest that organizational online participation is a promising tool to enhance employee involvement, driving innovations and enabling organizational transformation

Ideate. Collaborate. Repeat. A Research Agenda for Idea Generation, Collaboration and Evaluation in Open Innovation

Open innovation has been and remains to be a rapidly changing field of research in Information Systems and various other disciplines. With the rise of professional open innovation platforms and the emergence of crowdsourcing as well as employee-driven innovation, studies on the front-end of open innovation – namely idea generation, collaboration and evaluation – are facing new challenges. In this structured literature review, we analyze a large body of prior research in order to derive a framework, which is able to classify and reflect the lively debate on open innovation. In addition, we identify important implications for practitioners with advise on the design of open innovation systems. Moreover, our study identifies several promising areas for future research

When Life Gives You Lemons: How rating scales affect user activity and frustration in collaborative evaluation processes

Initiators of open innovation processes involving customers or employees often face vast amounts of idea proposals. These proposals vary greatly in terms of quality, which is why organizers often engage the users themselves in the evaluation process. Building on the concept of information overload, we evaluate the effects of three distinct rating scales on users’ activity and frustration measures. On the basis of an open innovation campaign for employees of a public-private institution in Germany, we systematically compare the novel “bag of lemons” method with conventional Likert scales and up-down-voting schemes. Our results demonstrate that the “bag of lemons”-approach yields higher levels of user activity, but is also perceived as significantly more frustrating. We find this effect to be fully mediated by perceived information overload, which points to potential avenues for the design of stimulating yet tolerably complex Information Systems for open innovation and rating techniques

Pattern Formation on Networks:from Localised Activity to Turing Patterns

Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important for understanding many natural phenomena. The emergence of patterns of activity on complex networks with reaction-diffusion dynamics on the nodes is studied here. The connection between solutions with a single activated node, which can bifurcate from an undifferentiated state, and the fully developed system-scale patterns are investigated computationally. The different coexisting patterns of activity the network can exhibit are shown to be connected via a snaking type bifurcation structure, similar to those responsible for organising localised pattern formation in regular lattices. These results reveal the origin of the multistable patterns found in systems organised on complex networks. A key role is found to be played by nodes with so called {\em optimal degree}, on which the interaction between the reaction kinetics and the network structure organise the behaviour of the system. A statistical representation of the density of solutions over the parameter space is used as a means to answer important questions about the number of accessible states that can be exhibited in systems with such a high degree of complexity