TY - JOUR A1 - Marwan, Norbert T1 - Challenges and perspectives in recurrence analyses of event time series JF - Frontiers in applied mathematics and statistics N2 - The analysis of event time series is in general challenging. Most time series analysis tools are limited for the analysis of this kind of data. Recurrence analysis, a powerful concept from nonlinear time series analysis, provides several opportunities to work with event data and even for the most challenging task of comparing event time series with continuous time series. Here, the basic concept is introduced, the challenges are discussed, and the future perspectives are summarized. KW - event time series KW - extreme events KW - recurrence analysis KW - edit distance KW - synchronization Y1 - 2023 U6 - https://doi.org/10.3389/fams.2023.1129105 SN - 2297-4687 VL - 9 PB - Frontiers Media CY - Lausanne ER - TY - JOUR A1 - Pikovskij, Arkadij T1 - Synchronization of oscillators with hyperbolic chaotic phases JF - Izvestija vysšich učebnych zavedenij : naučno-techničeskij žurnal = Izvestiya VUZ. Prikladnaja nelinejnaja dinamika = Applied nonlinear dynamics N2 - Topic and aim. Synchronization in populations of coupled oscillators can be characterized with order parameters that describe collective order in ensembles. A dependence of the order parameter on the coupling constants is well-known for coupled periodic oscillators. The goal of the study is to extend this analysis to ensembles of oscillators with chaotic phases, moreover with phases possessing hyperbolic chaos. Models and methods. Two models are studied in the paper. One is an abstract discrete-time map, composed with a hyperbolic Bernoulli transformation and with Kuramoto dynamics. Another model is a system of coupled continuous-time chaotic oscillators, where each individual oscillator has a hyperbolic attractor of Smale-Williams type. Results. The discrete-time model is studied with the Ott-Antonsen ansatz, which is shown to be invariant under the application of the Bernoulli map. The analysis of the resulting map for the order parameter shows, that the asynchronouis state is always stable, but the synchronous one becomes stable above a certain coupling strength. Numerical analysis of the continuous-time model reveals a complex sequence of transitions from an asynchronous state to a completely synchronous hyperbolic chaos, with intermediate stages that include regimes with periodic in time mean field, as well as with weakly and strongly irregular mean field variations. Discussion. Results demonstrate that synchronization of systems with hyperbolic chaos of phases is possible, although a rather strong coupling is required. The approach can be applied to other systems of interacting units with hyperbolic chaotic dynamics. N2 - Тема и цель. Синхронизация в популяциях связанных осцилляторов может быть охарактеризована параметрами порядка, описывающими коллективный порядок в ансамблях. Зависимость параметра порядка от коэффициентов связи хорошо известна для связанных периодических осцилляторов. Целью данного исследования является обобщение этого анализа на ансамбли осцилляторов с хаотическими фазами, а именно, с фазами, распределёнными на гиперболическом аттракторе. Модели и методы. В работе исследуются две модели. Первая – абстрактное отображение в дискретном времени, составленное из гиперболического преобразования Бернулли и динамики Курамото. Вторая – это система связанных хаотических осцилляторов в непрерывном времени, где каждый отдельный осциллятор имеет гиперболический аттрактор типа Смейла–Вильямса. Результаты. Модель в дискретном времени изучается с помощью подхода Отта–Антонсена, который, как показано, инвариантен при применении отображения Бернулли. Анализ полученного отображения по параметрам порядка показывает, что асинхронное состояние всегда устойчиво, а синхронное состояние становится устойчивым выше определенной силы связи. Численный анализ модели в непрерывном времени показывает сложную последовательность переходов из асинхронного состояния в полностью синхронный гиперболический хаос с промежуточными стадиями, которые включают режимы с периодическим во времени средним полем, а также со слабо и сильно нерегулярными вариациями среднего поля. Обсуждение. Результаты показывают, что синхронизация систем с гиперболическим фазовым хаосом возможна, хотя требуется довольно сильная связь. Данный подход может быть применен и к другим системам взаимодействующих звеньев с гиперболической хаотической динамикой. T2 - Синхронизация осцилляторов с гиперболическими хаотическими фазами KW - hyperbolic attractor KW - synchronization KW - collective dynamics KW - иперболический аттрактор KW - синхронизация KW - оллективная динамика Y1 - 2021 U6 - https://doi.org/10.18500/0869-6632-2021-29-1-78-87 SN - 0869-6632 SN - 2542-1905 VL - 29 IS - 1 SP - 78 EP - 87 PB - Saratov State University CY - Saratov ER - TY - JOUR A1 - Pikovskij, Arkadij T1 - Transition to synchrony in chiral active particles JF - Journal of physics. Complexity N2 - I study deterministic dynamics of chiral active particles in two dimensions. Particles are considered as discs interacting with elastic repulsive forces. An ensemble of particles, started from random initial conditions, demonstrates chaotic collisions resulting in their normal diffusion. This chaos is transient, as rather abruptly a synchronous collisionless state establishes. The life time of chaos grows exponentially with the number of particles. External forcing (periodic or chaotic) is shown to facilitate the synchronization transition. KW - active particles KW - chirality KW - synchronization KW - chaos KW - transient chaos Y1 - 2021 U6 - https://doi.org/10.1088/2632-072X/abdadb SN - 2632-072X VL - 2 IS - 2 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Ocampo-Espindola, Jorge Luis A1 - Omel'chenko, Oleh A1 - Kiss, Istvan Z. T1 - Non-monotonic transients to synchrony in Kuramoto networks and electrochemical oscillators JF - Journal of physics. Complexity N2 - We performed numerical simulations with the Kuramoto model and experiments with oscillatory nickel electrodissolution to explore the dynamical features of the transients from random initial conditions to a fully synchronized (one-cluster) state. The numerical simulations revealed that certain networks (e.g., globally coupled or dense Erdos-Renyi random networks) showed relatively simple behavior with monotonic increase of the Kuramoto order parameter from the random initial condition to the fully synchronized state and that the transient times exhibited a unimodal distribution. However, some modular networks with bridge elements were identified which exhibited non-monotonic variation of the order parameter with local maximum and/or minimum. In these networks, the histogram of the transients times became bimodal and the mean transient time scaled well with inverse of the magnitude of the second largest eigenvalue of the network Laplacian matrix. The non-monotonic transients increase the relative standard deviations from about 0.3 to 0.5, i.e., the transient times became more diverse. The non-monotonic transients are related to generation of phase patterns where the modules are synchronized but approximately anti-phase to each other. The predictions of the numerical simulations were demonstrated in a population of coupled oscillatory electrochemical reactions in global, modular, and irregular tree networks. The findings clarify the role of network structure in generation of complex transients that can, for example, play a role in intermittent desynchronization of the circadian clock due to external cues or in deep brain stimulations where long transients are required after a desynchronization stimulus. KW - synchronization KW - networks KW - Kuramoto model KW - electrochemistry KW - chemical KW - oscillations Y1 - 2021 U6 - https://doi.org/10.1088/2632-072X/abe109 SN - 2632-072X VL - 2 IS - 1 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Omelʹchenko, Oleh E. T1 - Nonstationary coherence-incoherence patterns in nonlocally coupled heterogeneous phase oscillators JF - Chaos : an interdisciplinary journal of nonlinear science N2 - We consider a large ring of nonlocally coupled phase oscillators and show that apart from stationary chimera states, this system also supports nonstationary coherence-incoherence patterns (CIPs). For identical oscillators, these CIPs behave as breathing chimera states and are found in a relatively small parameter region only. It turns out that the stability region of these states enlarges dramatically if a certain amount of spatially uniform heterogeneity (e.g., Lorentzian distribution of natural frequencies) is introduced in the system. In this case, nonstationary CIPs can be studied as stable quasiperiodic solutions of a corresponding mean-field equation, formally describing the infinite system limit. Carrying out direct numerical simulations of the mean-field equation, we find different types of nonstationary CIPs with pulsing and/or alternating chimera-like behavior. Moreover, we reveal a complex bifurcation scenario underlying the transformation of these CIPs into each other. These theoretical predictions are confirmed by numerical simulations of the original coupled oscillator system. KW - chimera states KW - synchronization KW - networks KW - Kuramoto KW - populations KW - dynamics KW - bumps KW - model Y1 - 2020 U6 - https://doi.org/10.1063/1.5145259 SN - 1054-1500 SN - 1089-7682 VL - 30 IS - 4 PB - American Institute of Physics CY - Melville ER - TY - GEN A1 - Bolotov, Maxim A1 - Smirnov, Lev A. A1 - Osipov, Grigory V. A1 - Pikovskij, Arkadij T1 - Complex chimera states in a nonlinearly coupled oscillatory medium T2 - 2018 2nd School on Dynamics of Complex Networks and their Application in Intellectual Robotics (DCNAIR) N2 - We consider chimera states in a one-dimensional medium of nonlinear nonlocally coupled phase oscillators. Stationary inhomogeneous solutions of the Ott-Antonsen equation for a complex order parameter that correspond to fundamental chimeras have been constructed. Stability calculations reveal that only some of these states are stable. The direct numerical simulation has shown that these structures under certain conditions are transformed to breathing chimera regimes because of the development of instability. Further development of instability leads to turbulent chimeras. KW - phase oscillator KW - nonlocal coupling KW - synchronization KW - chimera state KW - partial synchronization KW - phase lag KW - nonlinear dynamics Y1 - 2018 SN - 978-1-5386-5818-5 U6 - https://doi.org/10.1109/DCNAIR.2018.8589210 SP - 17 EP - 20 PB - IEEE CY - New York ER - TY - THES A1 - Omelchenko, Oleh T1 - Synchronität-und-Unordnung-Muster in Netzwerken gekoppelter Oszillatoren T1 - Patterns of synchrony and disorder in networks of coupled oscillators N2 - Synchronization of coupled oscillators manifests itself in many natural and man-made systems, including cyrcadian clocks, central pattern generators, laser arrays, power grids, chemical and electrochemical oscillators, only to name a few. The mathematical description of this phenomenon is often based on the paradigmatic Kuramoto model, which represents each oscillator by one scalar variable, its phase. When coupled, phase oscillators constitute a high-dimensional dynamical system, which exhibits complex behaviour, ranging from synchronized uniform oscillation to quasiperiodicity and chaos. The corresponding collective rhythms can be useful or harmful to the normal operation of various systems, therefore they have been the subject of much research. Initially, synchronization phenomena have been studied in systems with all-to-all (global) and nearest-neighbour (local) coupling, or on random networks. However, in recent decades there has been a lot of interest in more complicated coupling structures, which take into account the spatially distributed nature of real-world oscillator systems and the distance-dependent nature of the interaction between their components. Examples of such systems are abound in biology and neuroscience. They include spatially distributed cell populations, cilia carpets and neural networks relevant to working memory. In many cases, these systems support a rich variety of patterns of synchrony and disorder with remarkable properties that have not been observed in other continuous media. Such patterns are usually referred to as the coherence-incoherence patterns, but in symmetrically coupled oscillator systems they are also known by the name chimera states. The main goal of this work is to give an overview of different types of collective behaviour in large networks of spatially distributed phase oscillators and to develop mathematical methods for their analysis. We focus on the Kuramoto models for one-, two- and three-dimensional oscillator arrays with nonlocal coupling, where the coupling extends over a range wider than nearest neighbour coupling and depends on separation. We use the fact that, for a special (but still quite general) phase interaction function, the long-term coarse-grained dynamics of the above systems can be described by a certain integro-differential equation that follows from the mathematical approach called the Ott-Antonsen theory. We show that this equation adequately represents all relevant patterns of synchrony and disorder, including stationary, periodically breathing and moving coherence-incoherence patterns. Moreover, we show that this equation can be used to completely solve the existence and stability problem for each of these patterns and to reliably predict their main properties in many application relevant situations. N2 - Die Synchronisation von gekoppelten Oszillatoren tritt in vielen natürlichen und künstlichen Systemen auf, beispielsweise bei zirkadianen Uhren, zentralen Mustergeneratoren, Laserarrays, Stromnetzen oder chemischen und elektrochemischen Oszillatoren, um nur einige zu nennen. Die mathematische Beschreibung dieses Phänomens basiert häufig auf dem paradigmatischen Kuramoto-Modell, das jeden Oszillator durch eine skalare Variable, seine Phase, darstellt. Wenn Phasenoszillatoren gekoppelt sind, bilden sie ein hochdimensionales dynamisches System, das ein komplexes Verhalten aufweist, welches von synchronisierter kollektiver Oszillation bis zu Quasiperiodizität und Chaos reicht. Die entsprechenden kollektiven Rhythmen können für den normalen Betrieb verschiedener Systeme nützlich oder schädlich sein, weshalb sie Gegenstand zahlreicher Untersuchungen waren. Anfänglich wurden Synchronisationsphänomene in Systemen mit globaler Mittelfeldkopplung und lokaler Nächster-Nachbar Kopplung oder in komplexen Netzwerken untersucht. In den letzten Jahrzehnten gab es jedoch großes Interesse an anderen Kopplungsstrukturen, die die räumlich verteilte Natur realer Oszillatorsysteme und die entfernungsabhängige Natur der Wechselwirkung zwischen ihren Komponenten berücksichtigen. Sowohl in Bereichen der Biologie als auch der Neurowissenschaften gibt es eine Vielzahl von Beipsieln für solche Systeme. Dazu gehören räumlich verteilte Zellpopulationen, Zilien-Teppiche und neuronale Netze, die für das Arbeitsgedächtnis relevant sind. In vielen Fällen unterstützen diese Systeme eine Vielzahl von Synchronität-und-Unordnung-Mustern mit bemerkenswerten Eigenschaften, die in anderen kontinuierlichen Medien nicht beobachtet wurden. Solche Muster werden üblicherweise als Kohärenz-Inkohärenz-Muster bezeichnet, aber in symmetrisch gekoppelten Oszillatorsystemen sind diese auch unter dem Namen Chimära-Zustände bekannt. Das Hauptziel dieser Arbeit ist es, einen Überblick über verschiedene Arten von kollektivem Verhalten in großen Netzwerken räumlich verteilter Phasenoszillatoren zu geben und mathematische Methoden für deren Analyse zu entwickeln. Wir konzentrieren uns dabei auf die Kuramoto-Modelle für ein-, zwei- und dreidimensionale Oszillator-Arrays mit nichtlokaler Kopplung, wobei sich die Kopplung über einen Bereich erstreckt, welcher breiter ist als die Kopplung zum nächsten Nachbarn und von der Trennung abhängt. Wir verwenden die Tatsache, dass für eine spezielle (aber immer noch recht allgemeine) Phasenwechselwirkungsfunktion die langfristige grobkörnige Dynamik der obigen Systeme durch eine bestimmte Integro-Differentialgleichung beschrieben werden kann. Diese ergibt sich aus dem mathematischen Ansatz namens Ott-Antonsen-Theorie. Wir zeigen, dass diese Gleichung alle relevanten Synchronität-und-Unordnung-Muster angemessen darstellt, einschließlich stationärer, periodisch oszillierender und sich bewegender Kohärenz-Inkohärenz-Muster. Darüber hinaus zeigen wir, dass diese Gleichung verwendet werden kann, um das Existenz- und Stabilitätsproblem für jedes dieser Muster vollständig zu lösen und ihre Haupteigenschaften in vielen anwendungsrelevanten Situationen zuverlässig vorherzusagen. KW - phase oscillators KW - networks KW - synchronization KW - dynamical patterns KW - chimera states KW - Phasenoszillatoren KW - Netzwerke KW - Synchronisation KW - dynamische Muster KW - Chimäre-Zustände Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-535961 ER - TY - GEN A1 - Schaefer, Laura A1 - Bittmann, Frank T1 - Paired personal interaction reveals objective differences between pushing and holding isometric muscle action T2 - Postprints der Universität Potsdam : Humanwissenschaftliche Reihe N2 - In sports and movement sciences isometric muscle function is usually measured by pushing against a stable resistance. However, subjectively one can hold or push isometrically. Several investigations suggest a distinction of those forms. The aim of this study was to investigate whether these two forms of isometric muscle action can be distinguished by objective parameters in an interpersonal setting. 20 subjects were grouped in 10 same sex pairs, in which one partner should perform the pushing isometric muscle action (PIMA) and the other partner executed the holding isometric muscle action (HIMA). The partners had contact at the distal forearms via an interface, which included a strain gauge and an acceleration sensor. The mechanical oscillations of the triceps brachii (MMGtri) muscle, its tendon (MTGtri) and the abdominal muscle (MMGobl) were recorded by a piezoelectric-sensor-based measurement system. Each partner performed three 15s (80% MVIC) and two fatiguing trials (90% MVIC) during PIMA and HIMA, respectively. Parameters to compare PIMA and HIMA were the mean frequency, the normalized mean amplitude, the amplitude variation, the power in the frequency range of 8 to 15 Hz, a special power-frequency ratio and the number of task failures during HIMA or PIMA (partner who quit the task). A “HIMA failure” occurred in 85% of trials (p < 0.001). No significant differences between PIMA and HIMA were found for the mean frequency and normalized amplitude. The MMGobl showed significantly higher values of amplitude variation (15s: p = 0.013; fatiguing: p = 0.007) and of power-frequency-ratio (15s: p = 0.040; fatiguing: p = 0.002) during HIMA and a higher power in the range of 8 to 15 Hz during PIMA (15s: p = 0.001; fatiguing: p = 0.011). MMGtri and MTGtri showed no significant differences. Based on the findings it is suggested that a holding and a pushing isometric muscle action can be distinguished objectively, whereby a more complex neural control is assumed for HIMA. T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - 714 KW - neural-control KW - task failure KW - lengthening contractions KW - force KW - oscillations KW - load KW - time KW - synchronization KW - activation KW - principles Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-519119 SN - 1866-8364 IS - 714 ER - TY - JOUR A1 - Schaefer, Laura A1 - Bittmann, Frank T1 - Paired personal interaction reveals objective differences between pushing and holding isometric muscle action JF - PLOS One N2 - In sports and movement sciences isometric muscle function is usually measured by pushing against a stable resistance. However, subjectively one can hold or push isometrically. Several investigations suggest a distinction of those forms. The aim of this study was to investigate whether these two forms of isometric muscle action can be distinguished by objective parameters in an interpersonal setting. 20 subjects were grouped in 10 same sex pairs, in which one partner should perform the pushing isometric muscle action (PIMA) and the other partner executed the holding isometric muscle action (HIMA). The partners had contact at the distal forearms via an interface, which included a strain gauge and an acceleration sensor. The mechanical oscillations of the triceps brachii (MMGtri) muscle, its tendon (MTGtri) and the abdominal muscle (MMGobl) were recorded by a piezoelectric-sensor-based measurement system. Each partner performed three 15s (80% MVIC) and two fatiguing trials (90% MVIC) during PIMA and HIMA, respectively. Parameters to compare PIMA and HIMA were the mean frequency, the normalized mean amplitude, the amplitude variation, the power in the frequency range of 8 to 15 Hz, a special power-frequency ratio and the number of task failures during HIMA or PIMA (partner who quit the task). A “HIMA failure” occurred in 85% of trials (p < 0.001). No significant differences between PIMA and HIMA were found for the mean frequency and normalized amplitude. The MMGobl showed significantly higher values of amplitude variation (15s: p = 0.013; fatiguing: p = 0.007) and of power-frequency-ratio (15s: p = 0.040; fatiguing: p = 0.002) during HIMA and a higher power in the range of 8 to 15 Hz during PIMA (15s: p = 0.001; fatiguing: p = 0.011). MMGtri and MTGtri showed no significant differences. Based on the findings it is suggested that a holding and a pushing isometric muscle action can be distinguished objectively, whereby a more complex neural control is assumed for HIMA. KW - neural-control KW - task failure KW - lengthening contractions KW - force KW - oscillations KW - load KW - time KW - synchronization KW - activation KW - principles Y1 - 2021 U6 - https://doi.org/10.1371/journal.pone.0238331 SN - 1932-6203 VL - 16 IS - 5 PB - PLOS CY - San Francisco ER - TY - JOUR A1 - van Velzen, Ellen A1 - Thieser, Tamara A1 - Berendonk, Thomas U. A1 - Weitere, Markus A1 - Gaedke, Ursula T1 - Inducible defense destabilizes predator–prey dynamics BT - the importance of multiple predators JF - Oikos N2 - Phenotypic plasticity in prey can have a dramatic impact on predator-prey dynamics, e.g. by inducible defense against temporally varying levels of predation. Previous work has overwhelmingly shown that this effect is stabilizing: inducible defenses dampen the amplitudes of population oscillations or eliminate them altogether. However, such studies have neglected scenarios where being protected against one predator increases vulnerability to another (incompatible defense). Here we develop a model for such a scenario, using two distinct prey phenotypes and two predator species. Each prey phenotype is defended against one of the predators, and vulnerable to the other. In strong contrast with previous studies on the dynamic effects of plasticity involving a single predator, we find that increasing the level of plasticity consistently destabilizes the system, as measured by the amplitude of oscillations and the coefficients of variation of both total prey and total predator biomasses. We explain this unexpected and seemingly counterintuitive result by showing that plasticity causes synchronization between the two prey phenotypes (and, through this, between the predators), thus increasing the temporal variability in biomass dynamics. These results challenge the common view that plasticity should always have a stabilizing effect on biomass dynamics: adding a single predator-prey interaction to an established model structure gives rise to a system where different mechanisms may be at play, leading to dramatically different outcomes. KW - phenotypic plasticity KW - inducible defense KW - stability KW - synchronization KW - predator-prey dynamics Y1 - 2018 U6 - https://doi.org/10.1111/oik.04868 SN - 0030-1299 SN - 1600-0706 VL - 127 IS - 11 SP - 1551 EP - 1562 PB - Wiley CY - Hoboken ER -