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Chaotic channel
(2005)
This work combines the theory of chaotic synchronization with the theory of information in order to introduce the chaotic channel, an active medium formed by connected chaotic systems. This subset of a large chaotic net represents the path along which information flows. We show that the possible amount of information exchange between the transmitter, where information enters the net, and the receiver, the destination of the information, is proportional to the level of synchronization between these two special subsystems
We analyse a generic bottom-up nutrient phytoplankton model to help understand the dynamics of seasonally recurring algae blooms. The deterministic model displays a wide spectrum of dynamical behaviours, from simple cyclical blooms which trigger annually, to irregular chaotic blooms in which both the time between outbreaks and their magnitudes are erratic. Unusually, despite the persistent seasonal forcing, it is extremely difficult to generate blooms that are both annually recurring and also chaotic or irregular (i.e. in amplitude) even though this characterizes many real time series. Instead the model has a tendency to `skip' with outbreaks often being suppressed from one year to the next. This behaviour is studied in detail and we develop an analytical expression to describe the model's flow in phase space, yielding insights into the mechanism of the bloom recurrence. We also discuss how modifications to the equations through the inclusion of appropriate functional forms can generate more realistic dynamics.
We present an automatic control method for phase locking of regular and chaotic non-identical oscillations, when all subsystems interact via feedback. This method is based on the well known principle of feedback control which takes place in nature and is successfully used in engineering. In contrast to unidirectional and bidirectional coupling, the approach presented here supposes the existence of a special controller, which allows to change the parameters of the controlled systems. First we discuss general principles of automatic phase synchronization (PS) for arbitrary coupled systems with a controller whose input is given by a special quadratic form of coordinates of the individual systems and its output is a result of the application of a linear differential operator. We demonstrate the effectiveness of our approach for controlled PS on several examples: (i) two coupled regular oscillators, (ii) coupled regular and chaotic oscillators, (iii) two coupled chaotic R"ossler oscillators, (iv) two coupled foodweb models, (v) coupled chaotic R"ossler and Lorenz oscillators, (vi) ensembles of locally coupled regular oscillators, (vii) ensembles of locally coupled chaotic oscillators, and (viii) ensembles of globally coupled chaotic oscillators.
We study the pattern formation in a lattice of locally coupled phase oscillators with quenched disorder. In the synchronized regime quasi regular concentric waves can arise which are induced by the disorder of the system. Maximal regularity is found at the edge of the synchronization regime. The emergence of the concentric waves is related to the symmetry breaking of the interaction function. An explanation of the numerically observed phenomena is given in a one- dimensional chain of coupled phase oscillators. Scaling properties, describing the target patterns are obtained.
Biologists use mathematical functions to model, understand, and predict nature. For most biological processes, however, the exact analytical form is not known. This is also true for one of the most basic life processes, the uptake of food or resources. We show that the use of a number of nearly indistinguishable functions, which can serve as phenomenological descriptors of resource uptake, may lead to alarmingly different dynamical behaviour in a simple community model. More specifically, we demonstrate that the degree of resource enrichment needed to destabilize the community dynamics depends critically on the mathematical nature of the uptake function.
We analytically establish and numerically show that anomalous frequency synchronization occurs in a pair of asymmetrically coupled chaotic space extended oscillators. The transition to anomalous behaviors is crucially dependent on asymmetries in the coupling configuration, while the presence of phase defects has the effect of enhancing the anomaly in frequency synchronization with respect to the case of merely time chaotic oscillators.
Correlated many-electron dynamics : application to inelastic electron scattering at a metal film
(2005)
The multiconfiguration time-dependent Hartree-Fock and the time-dependent configuration interaction singles method are applied to the correlated many-electron dynamics of a one-dimensional jellium model system. We study the scattering of an initially free electron at a model film in the framework of both approaches. In particular, both methods are compared with regard to how they describe the underlying physical processes, namely inelastic electron scattering, inverse photoemission, and electron impact ionization
We present a nonparametric way to retrieve an additive system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long-term predictions. We apply our method to a modified chaotic Chua oscillator in order to demonstrate its potential
We consider the effect of external noise on the dynamics of limit cycle oscillators. The Lyapunov exponent becomes negative under influence of small white noise, what means synchronization of two or more identical systems subject to common noise. We analytically study the effect of small nonidentities in the oscillators and in the noise, and derive statistical characteristics of deviations from the perfect synchrony. Large white noise can lead to desynchronization of oscillators, provided they are nonisochronous. This is demonstrated for the Van der Pol-Duffing system
The work presents low signal dielectric spectra of gold/copper phthalocyanine/magnesium and gold/copper phthalocyanine/gold sandwich systems in the 25 Hz-1 MHz frequency range. The performed analysis enables us to distinguish the electrode resistance and the lattice polarization from processes related with electric transport, such as charge carrier relaxation at space charge region of a barrier and charge carrier injection in dielectric response.
An approach is presented for coupled chaotic systems with weak coherent motion, from which we estimate the upper bound value for the absolute phase difference in phase synchronous states. This approach shows that synchronicity in phase implies synchronicity in the time of events, a characteristic explored to derive an equation to detect phase synchronization, based on the absolute difference between the time of these events. We demonstrate the potential use of this approach for the phase coherent and the funnel attractor of the Rossler system, as well as for the spiking/bursting Rulkov map.
Elastic properties and electromechanical coupling factor of inflated polypropylene ferroelectrets
(2006)
Relaxation processes at the glass transition in polyamide 11 : From rigidity to viscoelasticity
(2006)
Wachsende Filamentbündel
(2006)
Kopplung von Polyelektrolyten und geladenen Lipid-Monoschichten an der Wasser / Luft-Grenzflächen
(2006)
Understanding the functional dynamics of the mammalian brain is one of the central aims of modern neuroscience. Mathematical modeling and computational simulations of neural networks can help in this quest. In recent publications, a multilevel model has been presented to simulate the resting-state dynamics of the cortico-cortical connectivity of the mammalian brain. In the present work we investigate how much of the dynamical behavior of the multilevel model can be reproduced by a strongly simplified model. We find that replacing each cortical area by a single Rulkov map recreates the patterns of dynamical correlation of the multilevel model, while the outcome of other models and setups mainly depends on the local network properties, e. g. the input degree of each vertex. In general, we find that a simple simulation whose dynamics depends on the global topology of the whole network is far from trivial. A systematic analysis of different dynamical models and coupling setups is required.
Many real-world networks are characterized by adaptive changes in their topology depending on the state of their nodes. Here we study epidemic dynamics on an adaptive network, where the susceptibles are able to avoid contact with the infected by rewiring their network connections. This gives rise to assortative degree correlation, oscillations, hysteresis, and first order transitions. We propose a low-dimensional model to describe the system and present a full local bifurcation analysis. Our results indicate that the interplay between dynamics and topology can have important consequences for the spreading of infectious diseases and related applications
We report a noise-memory induced phase transition in an array of oscillatory neural systems, which leads to the suppression of synchronous oscillations and restoration of excitable dynamics. This phenomenon is caused by the systematic contributions of temporally correlated parametric noise, i.e., possessing a memory, which stabilizes a deterministically unstable fixed point. Changing the noise correlation time, a reentrant phase transition to noise- induced excitability is observed in a globally coupled array. Since noise-induced excitability implies the restoration of the ability to transmit information, associated spatiotemporal patterns are observed afterwards. Furthermore, an analytic approach to predict the systematic effects of exponentially correlated noise is presented and its results are compared with the simulations
Motivated by the successful Karlsruhe dynamo experiment, a relatively low-dimensional dynamo model is proposed. It is based on a strong truncation of the magnetohydrodynamic (MHD) equations with an external forcing of the Roberts type and the requirement that the model system satisfies the symmetries of the full MHD system, so that the first symmetry-breaking bifurcations can be captured. The backbone of the Roberts dynamo is formed by the Roberts flow, a helical mean magnetic field and another part of the magnetic field coupled to these two by triadic mode interactions. A minimum truncation model (MTM) containing only these energetically dominating primary mode triads is fully equivalent to the widely used first-order smoothing approximation. However, it is shown that this approach works only in the limit of small wave numbers of the excited magnetic field or small magnetic Reynolds numbers ($Rm ll 1$). To obtain dynamo action under more general conditions, secondary mode
There is strong observational evidence of shocks and clumping in radiation-driven stellar winds from hot, luminous stars. The resulting non nous monotonic velocity law allows for radiative coupling between distant locations, which is so far not accounted for in hydrodynamic wind simulations. In the present paper, we determine the Sobolev source function and radiative line force in the presence of radiative coupling in spherically symmetric flows, extending the geometry-free formalism of Rybicki & Hummer (1978, ApJ, 219, 654) to the case of three-point coupling, which can result from, e. g., corotating interaction regions, wind shocks, or mass overloading. For a simple model of an overloaded wind, we find that, surprisingly, the flow decelerates at all radii above a certain height when nonlocal radiative coupling is accounted for. We discuss whether radiation-driven winds might in general not be able to re- accelerate after a non monotonicity has occurred in the velocity law