Excitable Units Research Articles

Modulated escape from a metastable state driven by colored noise.

Many phenomena in nature are described by excitable systems driven by colored noise. The temporal correlations in the fluctuations hinder an analytical treatment. We here present a general method of reduction to a white-noise system, capturing the color of the noise by effective and time-dependent boundary conditions. We apply the formalism to a model of the excitability of neuronal membranes, the leaky integrate-and-fire neuron model, revealing an analytical expression for the linear response of the system valid up to moderate frequencies. The closed form analytical expression enables the characterization of the response properties of such excitable units and the assessment of oscillations emerging in networks thereof.

A Particle Filter for Dynamic State Estimation in Multi-Machine Systems With Detailed Models

Particle filters provide a general framework for dynamic state estimation (DSE) in nonlinear systems. The scope for particle filter-based DSE can be significantly enhanced by exploiting data from phasor measurement units (PMUs) when available at higher sampling frequencies. In this paper, we present a particle filtering approach to dynamically estimate the states of a synchronous generator in a multi-machine setting considering the excitation and prime mover control systems. The filter relies on typical output measurements assumed available from PMUs stationed at generator buses. The performance of the proposed filter is illustrated with dynamic simulations on IEEE 14-bus system including: 1) generators models with subtransient dynamics, 2) excitation units (IEEE DC1A, DC2A, AC5A), and 3) turbine-governor models (steam and hydro). The estimation accuracy of the proposed filter is assessed for three classes of disturbances assuming noisy PMUs' measurements and comparative results are presented with the unscented Kalman filter (UKF). The accuracy-computational burden trade-off is also analyzed and the results strengthen the feasibility of using particle filters for dynamic state estimation.

Constructive effects of diversity in a multi-neuron model of the homeostatic regulation of the sleep–wake cycle

As an instance of diversity-induced resonance and of the constructive role of heterogeneity in complex systems, here we study a generalized version of a physiologically-motivated sleep–wake cycle model taking into account the role of orexin [Patriarca et al. (2012) [16]; Postnova et al. (2009) [9]]. With respect to the versions of the model studied previously, here we consider systems containing both a set of orexin neurons — responsible for the production of orexin — and a set of glutaminergic neurons — representing mental activity or sleep depending on their firing or silent state, respectively — within some basic network topologies. The neurons of one or both types are diversified and it is shown how the interplay between the heterogeneous constituent units produces as an emergent effect the recovering or improving of the sleep-wake cycle. At a general level, the results obtained suggest that also systems with a dynamics driven by a homeostatic mechanism, with a time scale much longer than that of the constituent excitable units, may present diversity-induced resonance.

A closer look at the apparent correlation of structural and functional connectivity in excitable neural networks.

The relationship between the structural connectivity (SC) and functional connectivity (FC) of neural systems is a central focus in brain network science. It is an open question, however, how strongly the SC-FC relationship depends on specific topological features of brain networks or the models used for describing excitable dynamics. Using a basic model of discrete excitable units that follow a susceptible - excited - refractory dynamic cycle (SER model), we here analyze how functional connectivity is shaped by the topological features of a neural network, in particular its modularity. We compared the results obtained by the SER model with corresponding simulations by another well established dynamic mechanism, the Fitzhugh-Nagumo model, in order to explore general features of the SC-FC relationship. We showed that apparent discrepancies between the results produced by the two models can be resolved by adjusting the time window of integration of co-activations from which the FC is derived, providing a clearer distinction between co-activations and sequential activations. Thus, network modularity appears as an important factor shaping the FC-SC relationship across different dynamic models.

Optimization of Magnetic Excitation Unit in High Efficiency Magnetorheological Planarization and Experimental Study

Optimization of Magnetic Excitation Unit in High Efficiency Magnetorheological Planarization and Experimental Study

Magnetorheological polishing using a permanent magnetic yoke with straight air gap for ultra-smooth surface planarization

A permanent magnetic yoke with a straight air gap was developed as the magnetic excitation unit, in order to improve the efficiency of magnetorheological (MR) polishing for ultra-smooth surface planarization. Finite element modelling was used to simulate the magnetic performance of the newly developed yoke, which was found to agree well with the experimental measurement. With the developed MR polishing apparatus, the effects of trough speed, work and excitation gap width, particle concentration within the MR fluid and workpiece size on the material removal rate were systematically investigated. Final tests were performed on glass specimens to examine the polishing performance. The polishing area in the developed process was much larger than that of the conventional MR finishing process with a carrier wheel and ultra-smooth surface of 1nm in Ra was achieved.

Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations

We study the collective dynamics of noise-driven excitable elements, so-called active rotators. Crucially here, the natural frequencies and the individual coupling strengths are drawn from some joint probability distribution. Combining a mean-field treatment with a Gaussian approximation allows us to find examples where the infinite-dimensional system is reduced to a few ordinary differential equations. Our focus lies in the cooperative behavior in a population consisting of two parts, where one is composed of excitable elements, while the other one contains only self-oscillatory units. Surprisingly, excitable behavior in the whole system sets in only if the excitable elements have a smaller coupling strength than the self-oscillating units. In this way positive local correlations between natural frequencies and couplings shape the global behavior of mixed populations of excitable and oscillatory elements.

ChemInform Abstract: Coordination Chemistry‐Assembled Multicomponent Systems Built from a Gable‐Like Bis‐Porphyrin: Synthesis and Photophysical Properties

AbstractReview: 64 refs.

Manipulating coherence resonance in a quantum dot semiconductor laser via electrical pumping.

Excitability and coherence resonance are studied in a semiconductor quantum dot laser under short optical self-feedback. For low pump levels, these are observed close to a homoclinic bifurcation, which is in correspondence with earlier observations in quantum well lasers. However, for high pump levels, we find excitability close to a boundary crisis of a chaotic attractor. We demonstrate that in contrast to the homoclinic bifurcation the crisis and thus the excitable regime is highly sensitive to the pump current. The excitability threshold increases with the pump current, which permits to adjust the sensitivity of the excitable unit to noise as well as to shift the optimal noise strength, at which maximum coherence is observed. The shift adds up to more than one order of magnitude, which strongly facilitates experimental realizations.

Average dynamics of a finite set of coupled phase oscillators.

We study the solutions of a dynamical system describing the average activity of an infinitely large set of driven coupled excitable units. We compared their topological organization with that reconstructed from the numerical integration of finite sets. In this way, we present a strategy to establish the pertinence of approximating the dynamics of finite sets of coupled nonlinear units by the dynamics of its infinitely large surrogate.

Synchronization extends the life time of the desired behavior of globally coupled systems

Synchronization occurs widely in natural and technological world, but it has not been widely used to extend the life time of the desirable behavior of the coupled systems. Here we consider the globally coupled system consisting of n units and show that the initial synchronous state extends the lifetime of desired behavior of the coupled system in the case when the excitation of one or few units is suddenly (breakdown of energy supply) or gradually (as the effect of aging and fatigue) switched off. We give evidence that for the properly chosen coupling the energy transfer from the excited units allows unexcited units to operate in the desired manner. As proof of concept, we examine the system of coupled externally excited rotating pendula. After the partial excitation switch off the initial complete synchronization of all pendula is replaced by phase synchronization with a constant phase shift between the clusters of excited and unexcited pendula. Our results show that the described extension of the system's life time occurs for the wide range of coupling parameters and is robust to the external perturbations.

Full-scale experimental modal analysis of an arch dam: The first experience in Iran

Forced vibration field tests and finite-element studies were conducted on the Shahid Rajaee concrete arch dam in Northern Iran to determine the dynamic properties of the dam–reservoir–foundation system. The first forced vibration tests on the dam were performed with two different types of exciter units, with a limited maximum force, bolted on the dam crest for alternative in-phase and out-of-phase sequencing. Because of an insufficient number of recording sensors, two arrangements of sensors were used to cover sufficient points on the dam crest and one gallery during tests. Two kinds of vibration tests, on–off and frequency sweeping, were carried out on the dam. The primary natural frequencies of the coupled system for both symmetric and anti-symmetric vibration modes were approximated during on–off tests in two types of sequencing of exciters, in phase and out-of-phase, with a maximum frequency of 14Hz. The principal forced vibration tests were performed at precise resonant frequencies based on the results of the on–off tests in which sweeping around the approximated frequencies at 0.1Hz increments was performed. Baseline correction and suitable bandpass filtering were applied to the test records and then signal processing was carried out to compute the auto power, cross power and coherence spectra. Nine middle modes of vibration of the coupled system and corresponding damping ratios were estimated. The empirical results are compared against the results from calibrated finite-element modeling of the system using former ambient vibration tests, considering the dam–reservoir–foundation interaction effects. Good agreement is obtained between experimental and numerical results for eight middle modes of the dam–reservoir–foundation system.

Persistence and failure of mean-field approximations adapted to a class of systems of delay-coupled excitable units.

We consider the approximations behind the typical mean-field model derived for a class of systems made up of type II excitable units influenced by noise and coupling delays. The formulation of the two approximations, referred to as the Gaussian and the quasi-independence approximation, as well as the fashion in which their validity is verified, are adapted to reflect the essential properties of the underlying system. It is demonstrated that the failure of the mean-field model associated with the breakdown of the quasi-independence approximation can be predicted by the noise-induced bistability in the dynamics of the mean-field system. As for the Gaussian approximation, its violation is related to the increase of noise intensity, but the actual condition for failure can be cast in qualitative, rather than quantitative terms. We also discuss how the fulfillment of the mean-field approximations affects the statistics of the first return times for the local and global variables, further exploring the link between the fulfillment of the quasi-independence approximation and certain forms of synchronization between the individual units.

Stability, coherent spiking and synchronization in noisy excitable systems with coupling and internal delays

We study the onset and the adjustment of different oscillatory modes in a system of excitable units subjected to two forms of noise and delays cast as external or internal according to whether they are associated with inter- or intra-unit activity. Conditions for stability of a single unit are derived in case of the linearized perturbed system, whereas the interplay of noise and internal delay in shaping the oscillatory motion is analyzed by the method of statistical linearization. It is demonstrated that the internal delay, as well as its coaction with external noise, drive the unit away from the bifurcation controlled by the excitability parameter. For the pair of interacting units, it is shown that the external/internal character of noise primarily influences frequency synchronization and the competition between the noise-induced and delay-driven oscillatory modes, while coherence of firing and phase synchronization substantially depend on internal delay. Some of the important effects include: (i) loss of frequency synchronization under external noise; (ii) existence of characteristic regimes of entrainment, where under variation of coupling delay, the optimized unit (noise intensity fixed at resonant value) may be controlled by the adjustable unit (variable noise) and vice versa, or both units may become adjusted to coupling delay; (iii) phase synchronization achieved both for noise-induced and delay-driven modes.

Analytical and experimental study of two delay-coupled excitable units

We investigate the onset of time-periodic oscillations for a system of two identical delay-coupled excitable (nonoscillatory) units. We first analyze these solutions by using asymptotic methods. The oscillations are described as relaxation oscillations exhibiting successive slow and fast changes. The analysis highlights the determinant role of the delay during the fast transition layers. We then study experimentally a system of two coupled electronic circuits that is modeled mathematically by the same delay differential equations. We obtain quantitative agreements between analytical and experimental bifurcation diagrams.

Transformation of spiral wave to plan wave in the two layers of coupled excitable media

The dynamics of spiral waves in a two-layer coupled excitable medium is studied by using the Bär-Eiswirth model. The two layers of medium are connected via network, i.e., a excitable unit is selected in each column of an excitable medium as a central point, and all excitable units in the same column of a layer medium are connected only with the corresponding central point and its eight neighbors in the opposite medium. The numerical results show that when the coupling strength is appropriately small, the two coupled spiral waves via local coupling can achieve their synchronization. Increasing coupling strength will induce meandering and drifting of spiral waves, leading to a desynchrony between the coupled spiral waves. The spiral wave with the resting state, low frequency plan wave and irregular pattern are observed to coexist. The coupled spiral waves via the transformation of spiral wave to synchronous plane wave disappear if the coupling strength is appropriately chosen. The physical mechanisms behind these phenomena are discussed.

Synthesis of corrole–fullerene dyads via [4 + 2] cycloaddition reaction

Corrole–fullerene dyads were prepared by treating anthracene-functionalized corroles with fullerene. Photo physical study indicated that the excited corrole unit was quenched due to the introduction of fullerene.

Chemically regulating Rh(i)-Bodipy photoredox switches

The ability of Rh(I) centers to undergo photoinduced electron transfer from discrete metal orbitals to Bodipy fluorophores is mediated through reversible coordination chemistry.

Waveguide tapering for beam-width control in a waveguide transducer

In a waveguide transducer that transmits an ultrasonic wave through a waveguide unit to a test structure, it is most preferred to send a non-dispersive ultrasonic wave of a narrow beam width. However, there is an unresolved conflict between the generation of the non- or less-dispersive wave and the transmission of a narrow-beam wave into a test structure. Among others, the thickness of the waveguide unit in a waveguide transducer is the key variable determining these two conflicting criteria, but the use of a uniformly-thick waveguide of any thickness cannot fulfill the two conflicting criteria simultaneously. In this study, we propose a specially-engineered tapered waveguide unit for the simultaneous satisfaction. An excitation unit is installed at the end of the thin region of the tapered waveguide and generates only the lowest non-dispersive shear-horizontal wave. Then the generated wave propagates through the tapered region of the waveguide unit and reaches the thick region of the waveguide with insignificant mode conversion to higher modes. If the tapered waveguide is used, the surviving lowest mode in the thick region of the waveguide is shown to carry most of the transmitted power and is finally propagated into a test structure. Because the beam size of the propagated wave and the thickness of the contacting waveguide region are inversely related, the thick contacting region of the tapered waveguide ensures narrow beam width. Numerical and experimental investigations were performed to check the effectiveness of the proposed waveguide-tapering approach.

Extreme events in excitable systems and mechanisms of their generation

We study deterministic systems, composed of excitable units of FitzHugh-Nagumo type, that are capable of self-generating and self-terminating strong deviations from their regular dynamics without the influence of noise or parameter change. These deviations are rare, short-lasting, and recurrent and can therefore be regarded as extreme events. Employing a range of methods we analyze dynamical properties of the systems, identifying features in the systems' dynamics that may qualify as precursors to extreme events. We investigate these features and elucidate mechanisms that may be responsible for the generation of the extreme events.