@phdthesis{Fischer2022,
  author    = {Fischer, Jens Walter},
  title     = {Random dynamics in collective behavior - consensus, clustering \& extinction of populations},
  doi       = {10.25932/publishup-55372},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-553725},
  school      = {Universit{\"a}t Potsdam},
  pages     = {242},
  year      = {2022},
  abstract  = {The echo chamber model describes the development of groups in heterogeneous social networks. By heterogeneous social network we mean a set of individuals, each of whom represents exactly one opinion. The existing relationships between individuals can then be represented by a graph. The echo chamber model is a time-discrete model which, like a board game, is played in rounds. In each round, an existing relationship is randomly and uniformly selected from the network and the two connected individuals interact. If the opinions of the individuals involved are sufficiently similar, they continue to move closer together in their opinions, whereas in the case of opinions that are too far apart, they break off their relationship and one of the individuals seeks a new relationship. In this paper we examine the building blocks of this model. We start from the observation that changes in the structure of relationships in the network can be described by a system of interacting particles in a more abstract space. These reflections lead to the definition of a new abstract graph that encompasses all possible relational configurations of the social network. This provides us with the geometric understanding necessary to analyse the dynamic components of the echo chamber model in Part III. As a first step, in Part 7, we leave aside the opinions of the inidividuals and assume that the position of the edges changes with each move as described above, in order to obtain a basic understanding of the underlying dynamics. Using Markov chain theory, we find upper bounds on the speed of convergence of an associated Markov chain to its unique stationary distribution and show that there are mutually identifiable networks that are not apparent in the dynamics under analysis, in the sense that the stationary distribution of the associated Markov chain gives equal weight to these networks. In the reversible cases, we focus in particular on the explicit form of the stationary distribution as well as on the lower bounds of the Cheeger constant to describe the convergence speed. The final result of Section 8, based on absorbing Markov chains, shows that in a reduced version of the echo chamber model, a hierarchical structure of the number of conflicting relations can be identified. We can use this structure to determine an upper bound on the expected absorption time, using a quasi-stationary distribution. This hierarchy of structure also provides a bridge to classical theories of pure death processes. We conclude by showing how future research can exploit this link and by discussing the importance of the results as building blocks for a full theoretical understanding of the echo chamber model. Finally, Part IV presents a published paper on the birth-death process with partial catastrophe. The paper is based on the explicit calculation of the first moment of a catastrophe. This first part is entirely based on an analytical approach to second degree recurrences with linear coefficients. The convergence to 0 of the resulting sequence as well as the speed of convergence are proved. On the other hand, the determination of the upper bounds of the expected value of the population size as well as its variance and the difference between the determined upper bound and the actual value of the expected value. For these results we use almost exclusively the theory of ordinary nonlinear differential equations.},
  language  = {en}
}
@phdthesis{Marwan2019,
  author    = {Marwan, Norbert},
  title     = {Recurrence plot techniques for the investigation of recurring phenomena in the system earth},
  isbn      = {978-3-00-064508-2},
  doi       = {10.25932/publishup-44197},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-441973},
  school      = {Universit{\"a}t Potsdam},
  pages     = {ix, 254},
  year      = {2019},
  abstract  = {The habilitation deals with the numerical analysis of the recurrence properties of geological and climatic processes. The recurrence of states of dynamical processes can be analysed with recurrence plots and various recurrence quantification options. In the present work, the meaning of the structures and information contained in recurrence plots are examined and described. New developments have led to extensions that can be used to describe the recurring patterns in both space and time. Other important developments include recurrence plot-based approaches to identify abrupt changes in the system's dynamics, to detect and investigate external influences on the dynamics of a system, the couplings between different systems, as well as a combination of recurrence plots with the methodology of complex networks. Typical problems in geoscientific data analysis, such as irregular sampling and uncertainties, are tackled by specific modifications and additions. The development of a significance test allows the statistical evaluation of quantitative recurrence analysis, especially for the identification of dynamical transitions. Finally, an overview of typical pitfalls that can occur when applying recurrence-based methods is given and guidelines on how to avoid such pitfalls are discussed. In addition to the methodological aspects, the application potential especially for geoscientific research questions is discussed, such as the identification and analysis of transitions in past climates, the study of the influence of external factors to ecological or climatic systems, or the analysis of landuse dynamics based on remote sensing data.},
  language  = {en}
}
@book{WilhelmHummelbrunnerCausemannetal.2015,
  author    = {Wilhelm, Jan Lorenz and Hummelbrunner, Richard and Causemann, Bernward and Mutter, Theo and Raab, Michaela and Bugenhagen, Anja and Smid, Hendrik},
  title     = {Evaluation komplexer Systeme},
  editor    = {Wilhelm, Jan Lorenz},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-336-7},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-78384},
  publisher      = {Universit{\"a}t Potsdam},
  pages     = {169},
  year      = {2015},
  abstract  = {Seit von Foerster k{\"o}nnen wir soziale Systeme als Black Boxes betrachten, zu deren Funktionsweise keine klaren Wenn-Dann-Aussagen m{\"o}glich erscheinen und deren Operationsweise sich f{\"u}r den Beobachter immer nur sequenziell und sprunghaft - und folglich nie ganzheitlich - darstellt. Jedes Bem{\"u}hen, ein soziales System tiefgr{\"u}ndig verstehen und abbilden zu wollen, kann somit schnell ein Gef{\"u}hl von Orientierungslosigkeit und {\"U}berforderung ausl{\"o}sen - {\"a}hnlich, wie w{\"a}hrend einer Achterbahnfahrt. F{\"u}r die Evaluationsdebatte resultiert aus dieser Sichtweise die Kernfrage, wie nun also im Rahmen von Evaluationen mit sozialer Komplexit{\"a}t umgegangen werden kann. An diese Frage ankn{\"u}pfend stellt der vorliegende Band das Feld der systemischen Therapie- und Beratungsans{\"a}tze als inspirierenden Fundus vor, aus welchem sich Konzepte, Methoden und Techniken zur Gestaltung von Evaluationsvorhaben ableiten lassen. Aber welche M{\"o}glichkeiten und Grenzen offenbaren sich dabei? L{\"a}sst sich sozialer Komplexit{\"a}t mit Hilfe dieser Ans{\"a}tze besser begegnen? Welche Rahmenbedingungen sollten dabei erf{\"u}llt sein und wie lassen sich systemische von nicht-systemischen Ans{\"a}tzen unterscheiden?},
  language  = {de}
}
@phdthesis{Topaj2001,
  author    = {Topaj, Dmitri},
  title     = {Synchronization transitions in complex systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-0000367},
  school      = {Universit{\"a}t Potsdam},
  year      = {2001},
  abstract  = {Gegenstand dieser Arbeit ist die Untersuchung generischer Synchronisierungsph{\"a}nomene in interagierenden komplexen Systemen. Diese Ph{\"a}nomene werden u.a. in gekoppelten deterministischen chaotischen Systemen beobachtet. Bei sehr schwachen Interaktionen zwischen individuellen Systemen kann ein {\"U}bergang zum schwach koh{\"a}renten Verhalten der Systeme stattfinden. In gekoppelten zeitkontinuierlichen chaotischen Systemen manifestiert sich dieser {\"U}bergang durch den Effekt der Phasensynchronisierung, in gekoppelten chaotischen zeitdiskreten Systemen durch den Effekt eines nichtverschwindenden makroskopischen Feldes. Der {\"U}bergang zur Koh{\"a}renz in einer Kette lokal gekoppelter Oszillatoren, beschrieben durch Phasengleichungen, wird im Bezug auf die Symmetrien des Systems untersucht. Es wird gezeigt, daß die durch die Symmetrien verursachte Reversibilit{\"a}t des Systems nichttriviale topologische Eigenschaften der Trajektorien bedingt, so daß das als dissipativ konstruierte System in einem ganzen Parameterbereich quasi-Hamiltonische Z{\"u}ge aufweist, d.h. das Phasenvolumen ist im Schnitt erhalten, und die Lyapunov-Exponenten sind paarweise symmetrisch. Der {\"U}bergang zur Koh{\"a}renz in einem Ensemble global gekoppelter chaotischer Abbildungen wird durch den Verlust der Stabilit{\"a}t des entkoppelten Zustandes beschrieben. Die entwickelte Methode besteht darin, die Selbstkonsistenz des makroskopischen Feldes aufzuheben, und das Ensemble in Analogie mit einem Verst{\"a}rkerschaltkreis mit R{\"u}ckkopplung durch eine komplexe lineare {\"U}bertragungssfunktion zu charakterisieren. Diese Theorie wird anschließend f{\"u}r einige theoretisch interessanten F{\"a}lle verallgemeinert.},
  language  = {en}
}