@article{WiesnerLadyman2021,
  author    = {Wiesner, Karoline and Ladyman, James},
  title     = {Complex systems are always correlated but rarely information processing},
  series = {Journal of physics. Complexity},
  volume    = {2},
  journal   = {Journal of physics. Complexity},
  number    = {4},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {2632-072X},
  doi       = {10.1088/2632-072X/ac371c},
  pages     = {4},
  year      = {2021},
  abstract  = {'Complex systems are information processors' is a statement that is frequently made. Here we argue for the distinction between information processing-in the sense of encoding and transmitting a symbolic representation-and the formation of correlations (pattern formation/self-organisation). The study of both uses tools from information theory, but the purpose is very different in each case: explaining the mechanisms and understanding the purpose or function in the first case, versus data analysis and correlation extraction in the latter. We give examples of both and discuss some open questions. The distinction helps focus research efforts on the relevant questions in each case.},
  language  = {en}
}
@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}
}
@misc{MotterMatiasKurthsetal.2006,
  author    = {Motter, Adilson E. and Matias, Manuel A. and Kurths, J{\"u}rgen and Ott, Edward},
  title     = {Dynamics on complex networks and applications},
  series = {Physica. D, Nonlinear phenomena},
  volume    = {224},
  journal   = {Physica. D, Nonlinear phenomena},
  number    = {1-2},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0167-2789},
  doi       = {10.1016/j.physd.2006.09.012},
  pages     = {VII -- VIII},
  year      = {2006},
  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}
}
@phdthesis{Bergner2011,
  author    = {Bergner, Andr{\´e}},
  title     = {Synchronization in complex systems with multiple time scales},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-53407},
  school      = {Universit{\"a}t Potsdam},
  year      = {2011},
  abstract  = {In the present work synchronization phenomena in complex dynamical systems exhibiting multiple time scales have been analyzed. Multiple time scales can be active in different manners. Three different systems have been analyzed with different methods from data analysis. The first system studied is a large heterogenous network of bursting neurons, that is a system with two predominant time scales, the fast firing of action potentials (spikes) and the burst of repetitive spikes followed by a quiescent phase. This system has been integrated numerically and analyzed with methods based on recurrence in phase space. An interesting result are the different transitions to synchrony found in the two distinct time scales. Moreover, an anomalous synchronization effect can be observed in the fast time scale, i.e. there is range of the coupling strength where desynchronization occurs. The second system analyzed, numerically as well as experimentally, is a pair of coupled CO₂ lasers in a chaotic bursting regime. This system is interesting due to its similarity with epidemic models. We explain the bursts by different time scales generated from unstable periodic orbits embedded in the chaotic attractor and perform a synchronization analysis of these different orbits utilizing the continuous wavelet transform. We find a diverse route to synchrony of these different observed time scales. The last system studied is a small network motif of limit cycle oscillators. Precisely, we have studied a hub motif, which serves as elementary building block for scale-free networks, a type of network found in many real world applications. These hubs are of special importance for communication and information transfer in complex networks. Here, a detailed study on the mechanism of synchronization in oscillatory networks with a broad frequency distribution has been carried out. In particular, we find a remote synchronization of nodes in the network which are not directly coupled. We also explain the responsible mechanism and its limitations and constraints. Further we derive an analytic expression for it and show that information transmission in pure phase oscillators, such as the Kuramoto type, is limited. In addition to the numerical and analytic analysis an experiment consisting of electrical circuits has been designed. The obtained results confirm the former findings.},
  language  = {en}
}
@misc{Dietrich2008,
  type      = {Master Thesis},
  author    = {Dietrich, Jan Philipp},
  title     = {Phase Space Reconstruction using the frequency domain : a generalization of actual methods},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-50738},
  school      = {Universit{\"a}t Potsdam},
  year      = {2008},
  abstract  = {Phase Space Reconstruction is a method that allows to reconstruct the phase space of a system using only an one dimensional time series as input. It can be used for calculating Lyapunov-exponents and detecting chaos. It helps to understand complex dynamics and their behavior. And it can reproduce datasets which were not measured. There are many different methods which produce correct reconstructions such as time-delay, Hilbert-transformation, derivation and integration. The most used one is time-delay but all methods have special properties which are useful in different situations. Hence, every reconstruction method has some situations where it is the best choice. Looking at all these different methods the questions are: Why can all these different looking methods be used for the same purpose? Is there any connection between all these functions? The answer is found in the frequency domain : Performing a Fourier transformation all these methods getting a similar shape: Every presented reconstruction method can be described as a multiplication in the frequency domain with a frequency-depending reconstruction function. This structure is also known as a filter. From this point of view every reconstructed dimension can be seen as a filtered version of the measured time series. It contains the original data but applies just a new focus: Some parts are amplified and other parts are reduced. Furthermore I show, that not every function can be used for reconstruction. In the thesis three characteristics are identified, which are mandatory for the reconstruction function. Under consideration of these restrictions one gets a whole bunch of new reconstruction functions. So it is possible to reduce noise within the reconstruction process itself or to use some advantages of already known reconstructions methods while suppressing unwanted characteristics of it.},
  language  = {en}
}
@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}
}