57 research outputs found
The transition between strong and weak chaos in delay systems: Stochastic modeling approach
Get PDF© 2015 American Physical Society. We investigate the scaling behavior of the maximal Lyapunov exponent in chaotic systems with time delay. In the large-delay limit, it is known that one can distinguish between strong and weak chaos depending on the delay scaling, analogously to strong and weak instabilities for steady states and periodic orbits. Here we show that the Lyapunov exponent of chaotic systems shows significant differences in its scaling behavior compared to constant or periodic dynamics due to fluctuations in the linearized equations of motion. We reproduce the chaotic scaling properties with a linear delay system with multiplicative noise. We further derive analytic limit cases for the stochastic model illustrating the mechanisms of the emerging scaling laws.This work was supported by a fellowship within the Postdoc-Programme of the German Academic Exchange Service (DAAD).Peer Reviewe
Mode hopping in oscillating systems with stochastic delays
Get PDFWe study a noisy oscillator with pulse delayed feedback, theoretically and in an electronic experimental implementation. Without noise, this system has multiple stable periodic regimes. We consider two types of noise: (i) phase noise acting on the oscillator state variable and (ii) stochastic fluctuations of the coupling delay. For both types of stochastic perturbations the system hops between the deterministic regimes, but it shows dramatically different scaling properties for different types of noise. The robustness to conventional phase noise increases with coupling strength. However for stochastic variations in the coupling delay, the lifetimes decrease exponentially with the coupling strength. We provide an analytic explanation for these scaling properties in a linearized model. Our findings thus indicate that the robustness of a system to stochastic perturbations strongly depends on the nature of these perturbations
Stochastic switching in delay-coupled oscillators
Get PDF© 2014 American Physical Society. A delay is known to induce multistability in periodic systems. Under influence of noise, coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns. For coupled phase oscillators we reduce the delay system to a nondelayed Langevin equation, which allows us to analytically compute the distribution of frequencies and their corresponding residence times. The number of stable periodic orbits scales with the roundtrip delay time and coupling strength, but the noisy system visits only a fraction of the orbits, which scales with the square root of the delay time and is independent of the coupling strength. In contrast, the residence time in the different orbits is mainly determined by the coupling strength and the number of oscillators, and only weakly dependent on the coupling delay. Finally we investigate the effect of a detuning between the oscillators. We demonstrate the generality of our results with delay-coupled FitzHugh-Nagumo oscillators.T.J. acknowledges support by a fellowship within the Postdoc-Programme of the German Academic Exchange Service (DAAD).Peer Reviewe
Multimedia, Costume and Textile Artistic Interpretation of Life and Work of Otti Berger
No full textOvaj diplomski rad posvećen je životu i djelu Otti Berger, umjetnice tekstilnog dizajna koja je ostavila dubok i trajan pečat u svijetu umjetnosti i dizajna. Kroz analizu njezina rada u Bauhausu, njezine inovacije u materijalima i tehnikama te njezino duboko razumijevanje narodnih nošnji i povijesti odijevanja, ovaj rad naglašava osobnu inspiraciju autorice rada za stvaranje vlastitih tekstilnih, kostimografskih i multimedijalnih umjetničkih rješenja. Ovaj diplomski rad predstavlja dizajn kostima za zamišljeni dokumentarno-umjetnički film o životu Otti Berger. Film, pa tako i inspiracija za kostime podijeljen je na tri dijela uzevši u obzir tri najbitnije faze Ottina života od rođenja do tragične smrti. U prvoj i trećoj fazi se kostimogafski poštuje povijesna dokumentirana točnost. Druga Bauhaus faza najveći je dio ovog rada jer autorica kreirala autorske kostimografske stilizacije koje se poigravaju s kreativnim miješanjem silueta ženskog odijevanja 1930-ih i Ottinim specifičnim tkanim uzorcima i tog vremena. Autorica rada dijeli i svoje iskustvo u stvaranja finalnog dizajna i izrade haljine inspirirane Ottinim radom kao svoj doprinos u očuvanju i širenju njezinog naslijeđa povezujući prošlost i sadašnjost, kreirajući korelaciju između tradicije i inovacije. Ovaj rad istražuje dubinu i širinu Otti Berger kao umjetnice i dizajnerice te ističe njezin trajni utjecaj na suvremeni dizajn mladih umjetnika.This thesis is dedicated to the life and work of Otti Berger, a textile designer who left a deep and lasting mark on the world of art and design. Through an analysis of her work at the Bauhaus, her innovations in materials and techniques, and her deep understanding of folk costumes and the history of clothing, this work highlights the author's personal inspiration for creating her own textile, costume and multimedia artistic solutions. This thesis presents the costume design for an imagined documentary-art film about the life of Otti Berger. The film, as well as the inspiration for the costumes, is divided into three parts, taking into account the three most important phases of Otti's life from birth to tragic death. In the first and third phase, the documented accuracy is respected in terms of costuming. The second Bauhaus phase is the largest part of this work, as the author created original costume stylizations that play with the creative mixing of silhouettes of women's clothing in the 1930s and Otta's specific woven patterns of that time. The author of the work also shares her experience in creating the final design and making of a dress inspired by Otta's work as her contribution to preserving and expanding her heritage by connecting the past and the present, creating a correlation between tradition and innovation. This paper explores the depth and breadth of Otti Berger as an artist and designer and highlights her lasting influence on contemporary design by young artists
Multimedia, Costume and Textile Artistic Interpretation of Life and Work of Otti Berger
No full textOvaj diplomski rad posvećen je životu i djelu Otti Berger, umjetnice tekstilnog dizajna koja je ostavila dubok i trajan pečat u svijetu umjetnosti i dizajna. Kroz analizu njezina rada u Bauhausu, njezine inovacije u materijalima i tehnikama te njezino duboko razumijevanje narodnih nošnji i povijesti odijevanja, ovaj rad naglašava osobnu inspiraciju autorice rada za stvaranje vlastitih tekstilnih, kostimografskih i multimedijalnih umjetničkih rješenja. Ovaj diplomski rad predstavlja dizajn kostima za zamišljeni dokumentarno-umjetnički film o životu Otti Berger. Film, pa tako i inspiracija za kostime podijeljen je na tri dijela uzevši u obzir tri najbitnije faze Ottina života od rođenja do tragične smrti. U prvoj i trećoj fazi se kostimogafski poštuje povijesna dokumentirana točnost. Druga Bauhaus faza najveći je dio ovog rada jer autorica kreirala autorske kostimografske stilizacije koje se poigravaju s kreativnim miješanjem silueta ženskog odijevanja 1930-ih i Ottinim specifičnim tkanim uzorcima i tog vremena. Autorica rada dijeli i svoje iskustvo u stvaranja finalnog dizajna i izrade haljine inspirirane Ottinim radom kao svoj doprinos u očuvanju i širenju njezinog naslijeđa povezujući prošlost i sadašnjost, kreirajući korelaciju između tradicije i inovacije. Ovaj rad istražuje dubinu i širinu Otti Berger kao umjetnice i dizajnerice te ističe njezin trajni utjecaj na suvremeni dizajn mladih umjetnika.This thesis is dedicated to the life and work of Otti Berger, a textile designer who left a deep and lasting mark on the world of art and design. Through an analysis of her work at the Bauhaus, her innovations in materials and techniques, and her deep understanding of folk costumes and the history of clothing, this work highlights the author's personal inspiration for creating her own textile, costume and multimedia artistic solutions. This thesis presents the costume design for an imagined documentary-art film about the life of Otti Berger. The film, as well as the inspiration for the costumes, is divided into three parts, taking into account the three most important phases of Otti's life from birth to tragic death. In the first and third phase, the documented accuracy is respected in terms of costuming. The second Bauhaus phase is the largest part of this work, as the author created original costume stylizations that play with the creative mixing of silhouettes of women's clothing in the 1930s and Otta's specific woven patterns of that time. The author of the work also shares her experience in creating the final design and making of a dress inspired by Otta's work as her contribution to preserving and expanding her heritage by connecting the past and the present, creating a correlation between tradition and innovation. This paper explores the depth and breadth of Otti Berger as an artist and designer and highlights her lasting influence on contemporary design by young artists
Noise-induced switching in an oscillator with pulse delayed feedback: a discrete stochastic modelling approach
Get PDFWe study the dynamics of an oscillatory system with pulse delayed feedback and noise of two types: i) phase noise acting on the oscillator and ii) stochastic fluctuations of the feedback delay. Using an event-based approach, we reduce the system dynamics to a stochastic discrete map. For weak noise we find that the oscillator fluctuates around a deterministic state, and we derive an autoregressive model describing the system dynamics. For stronger noise the oscillator demonstrates noise-induced switching between various deterministic states; our theory provides a good estimate of the switching statistics in the linear limit. We show that the robustness of the system towards this switching is strikingly different depending on the type of noise. We compare the analytical results for linear coupling to numerical simulations of nonlinear coupling, and find that the linear model also provides a qualitative explanation for the differences in robustness to both types of noise. Moreover, phase noise drives the system towards higher frequencies, while stochastic delays do not, and we relate this effect to our theoretical results
Autocorrelation properties of chaotic delay dynamical systems: A study on semiconductor lasers
Get PDF© 2014 American Physical Society. We present a detailed experimental characterization of the autocorrelation properties of a delayed feedback semiconductor laser for different dynamical regimes. We show that in many cases the autocorrelation function of laser intensity dynamics can be approximated by the analytically derived autocorrelation function obtained from a linear stochastic model with delay. We extract a set of dynamic parameters from the fit with the analytic solutions and discuss the limits of validity of our approximation. The linear model captures multiple fundamental properties of delay systems, such as the shift and asymmetric broadening of the different delay echoes. Thus, our analysis provides significant additional insight into the relevant physical and dynamical properties of delayed feedback lasers.This work was supported by Ministerio de Economía y Competitividad (MINECO, Spain) and Fondo Europeo del Desarrollo Regional (FEDER) via the Project No. TEC2012-36335 (TRIPHOP) and by Comunitat Autònoma de les Illes Balears via Grups Competitius. T.J. acknowledges support by a fellowship within the Postdoc-Programme of the German Academic Exchange Service (DAAD).Peer Reviewe
Synchronization and symmetry breaking of delay-coupled oscillators: on the role of phase and amplitude instabilities
No full textWe study the synchronization behavior of Stuart-Landau oscillators coupled with delay, using analytical and numerical methods. We compare the dynamics of one oscillator with delayed feedback, two mutually oscillators coupled with delay, and two delay-coupled elements with feedback. Taking only the phase dynamics into account, no chaotic dynamics has been observed. Moreover, the stability of the symmetric (identical synchronization) solution is the same in each of the three studied networks of delay-coupled elements. When allowing variable oscillation amplitude, the delay can induce amplitude instabilities. We provide analytical proof that, in case of two mutually coupled elements, the onset of an amplitude instability is accompanied by a symmetry breaking, leading to the in lasers observed leader-laggard behavior in the chaotic regime. Adding self-feedback (with the same strength and delay as the coupling), stabilizes the system in transverse directionO.D. acknowledges the Research Foundation Flanders (FWO-Vlaanderen) for a fellowship and for project support.
R.V. acknowledges the support of the Hertie Foundation. This work was partially supported by the
Interuniversity Attraction Poles program of the Belgian Science Policy Office, under grant IAP VI-10 ”photonics@
be” and by the European Community Project GABA (FP6-NEST contract 043309).Peer reviewe
Chaos synchronization by resonance of multiple delay times
Get PDFChaos synchronization may arise in networks of nonlinear units with delayed couplings. We study complete and sublattice synchronization generated by resonance of two large time delays with a specific ratio. As it is known for single-delay networks, the number of synchronized sublattices is determined by the greatest common divisor (GCD) of the network loop lengths. We demonstrate analytically the GCD condition in networks of iterated Bernoulli maps with multiple delay times and complement our analytic results by numerical phase diagrams, providing parameter regions showing complete and sublattice synchronization by resonance for Tent and Bernoulli maps. We compare networks with the same GCD with single and multiple delays, and we investigate the sensitivity of the correlation to a detuning between the delays in a network of coupled Stuart-Landau oscillators. Moreover, the GCD condition also allows detection of time-delay resonances, leading to high correlations in nonsynchronizable networks. Specifically, GCD-induced resonances are observed both in a chaotic asymmetric network and in doubly connected rings of delay-coupled noisy linear oscillators
Canard resonance: on noise-induced ordering of trajectories in heterogeneous networks of slow-fast systems
No full textInternational audienceWe analyze the dynamics of a network of semiconductor lasers coupled via their mean intensity through a nonlinear optoelectronic feedback loop. We establish experimentally the excitable character of a single node, which stems from the slow-fast nature of the system, adequately described by a set of rate equations with three well separated time scales. Beyond the excitable regime, the system undergoes relaxation oscillations where the nodes display canard dynamics. We show numerically that, without noise, the coupled system follows an intricate canard trajectory, with the nodes switching on one by one. While incorporating noise leads to a better correspondence between numerical simulations and experimental data, it also has an unexpected ordering effect on the canard orbit, causing the nodes to switch on closer together in time. We find that the dispersion of the trajectories of the network nodes in phase space is minimized for a non-zero noise strength, and call this phenomenon Canard Resonance
- …
