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Understanding the complex dynamics of cardio-respiratory coupling sheds light on the underlying mechanisms governing the communication between these two physiological systems. Previous research has predominantly considered the coupling at respiratory rates slower than the heart rate and shown that respiratory oscillations lead to modulation and/or synchronization of the heart rate. Whereas the mechanisms of cardio-respiratory communication are still under discussion, peripheral nervous regulation is considered to be the predominant factor. This work offers a novel experimental design and applies the concept of instantaneous phase to detect cardio-respiratory entrainment at elevated respiration rates, close to the resting heart rate. If such 1:1 entrainment exists, it would suggest direct neuronal communication between the respiration and heart centres in the brain. We have observed 1:1 entrainment in all volunteers, with consistently longer synchronization episodes seen in physically fitter people, and demonstrated that cardio-respiratory synchronization at both low and high respiration rates is associated with a common underlying communication mechanism.

Energy harvesting of ambient vibrations using a combination of a mechanical structure (oscillator) and an electrical transducer has become a valuable technique for powering small wireless sensors. Bistable mechanical oscillators have recently attracted the attention of researchers as they can be used to harvest energy within a wider band of frequencies. In this manuscript, the response of a bistable harvester to different forms of ambient vibration is analysed. In particular, harmonic noise, which has a narrow spectrum, similarly to harmonic signals, yet is stochastic, like broad-spectrum white noise, is considered. Links between bistable harvester responses and stochastic and vibrational resonance are explored., A contribution to a theme issue "Vibrational and stochastic resonance in driven nonlinear systems"

The complicated patterns of the single-channel currents in potassium ion channel KcsA are governed by the structural variability of the selectivity filter. A comparative analysis of the dynamics of the wild type KcsA channel and several of its mutants showing different conducting patterns was performed. A strongly correlated dynamical network of interacting residues is found to play a key role in regulating the state of the wild type channel. The network is centered on the aspartate D80 which plays the role of a hub by strong interacting via hydrogen bonds with residues E71, R64, R89, and W67. Residue D80 also affects the selectivity filter via its backbones. This network further compromises ions and water molecules located inside the channel that results in the mutual influence: the permeation depends on the configuration of residues in the network, and the dynamics of network&rsquo, s residues depends on locations of ions and water molecules inside the selectivity filter. Some features of the network provide a further understanding of experimental results describing the KcsA activity. In particular, the necessity of anionic lipids to be present for functioning the channel is explained by the interaction between the lipids and the arginine residues R64 and R89 that prevents destabilizing the structure of the selectivity filter.

Voltage-gated sodium channels (NaVs) play fundamental roles in eukaryotes, but their exceptional size hinders their structural resolution. Bacterial NaVs are simplified homologues of their eukaryotic counterparts, but their use as models of eukaryotic Na+ channels is limited by their homotetrameric structure at odds with the asymmetric Selectivity Filter (SF) of eukaryotic NaVs. This work aims at mimicking the SF of eukaryotic NaVs by engineering radial asymmetry into the SF of bacterial channels. This goal was pursued with two approaches: the co-expression of different monomers of the NaChBac bacterial channel to induce the random assembly of heterotetramers, and the concatenation of four bacterial monomers to form a concatemer that can be targeted by site-specific mutagenesis. Patch-clamp measurements and Molecular Dynamics simulations showed that an additional gating charge in the SF leads to a significant increase in Na+ and a modest increase in the Ca2+ conductance in the NavMs concatemer in agreement with the behavior of the population of random heterotetramers with the highest proportion of channels with charge &minus, 5e. We thus showed that charge, despite being important, is not the only determinant of conduction and selectivity, and we created new tools extending the use of bacterial channels as models of eukaryotic counterparts.

During running, interactions were considered between three physiological oscillators - the heart, breaths, and steps. During intense exercise, the oscillations of all three systems are close to regular, producing good conditions to observe and characterise synchronization. The origin, as well as any physiological significance, of synchronization between these systems during running is not fully accepted or understood. Furthermore, the impact on synchronization of controlling both breathing and step rate has not been previously reported in detail. This study aims to measure cardiolocomotor, cardiorespiratory and respiratory- locomotor synchronization during different running protocols. Breathing was controlled by taking a fixed number of steps per breath (ratios of 5:1 and 3:1). Step rate was then guided at rates close to active heart rate, to instigate 1:1 phase-locking. Instantaneous phase difference quantified synchronization episodes. We have successfully observed all three forms of synchronization during all running protocols. Furthermore, coupling between heartbeats and steps was more pronounced when step rate was guided, and both cardiorespiratory and respiratory-locomotor coupling were extended when breathing rate was fixed to steps. These are exciting initial results from a novel experimental design, highlighting the complex interconnection that exists between these three systems during running, and the conditions to best observe the phenomena.

Cardio-respiratory synchronization is a phenomenon of particular interest- especially at a 1:1 ratio- and may give greater insight into the underlying mechanisms of cardio-respiratory communication. Synchronization of this ratio is hypothesised to occur when breathing rate exceeds heart rate, which is the premise of this research. A novel experimental design focused on guiding elevated respiration to induce the entrainment of heart rate, and produce an equivalent rise in value. Application of instantaneous phase for identification and analysis of synchronization allowed for a reliable method of measuring the interaction between these stochastic processes. We have identified 1:1 phase synchronization in all volunteers measured. Longer synchronization episodes were observed reliably in athletic individuals, corroborating previous research for spontaneous breathing. This observation suggests that cardio-respiratory synchronization at all respiration rates is associated with a common underlying communication mechanism. Furthermore, it presents cardio-respiratory synchronization as a potential future measurement of fitness and autonomic health.\ud

In recent experimental studies, cardio-respiratory synchronisation was observed when the respiration rate was higher than the resting heart rate. Under this condition, there is a strong asymmetry in the synchronisation tongue towards frequencies higher than that of an unperturbed self-oscillator. These experimental results are compelling because they support a novel hypothesis about the interaction of cardiac and respiratory centres in the brain. This hypothesis, however, required further validation; we aimed to observe the key experimental features in related dynamical models. A number of simple self-oscillatory systems under an external driving force have been considered in this work, and a persistent sodium plus potassium neuron model was found to display the strong asymmetry, which is the key feature of the experimental observations. Bifurcations and other changes in the model’s state space were considered by varying the amplitude and frequency of the external force. It was shown that the strong asymmetry in the synchronisation tongue is linked to a non-uniformity of the surface of the non-synchronous invariant torus, and, within a certain range of parameters, to the additional saddle–node bifurcations of cycles. Then, it was demonstrated that the torus non-uniformity leads to changes in the shape of the phase difference potential as the amplitude increases. To illustrate the latter effect, a numerical approach for estimating the one dimensional phase difference profile and providing the corresponding explicit analytical expression is developed. Also, a discrepancy in synchronisation boundaries obtained by two different approaches, one based on bifurcational analysis and the other on a time series technique, was observed. The latter observation stresses the necessity of considering the standard deviation of instantaneous frequency alongside the mean value for the non-ambiguous identification of synchronisation in periodically driven systems.

We address the increase of electron drift velocity that arises in semiconductor superlattices (SLs) subjected to constant electric and magnetic fields. It occurs if the magnetic field possesses nonzero components both along and perpendicular to the SL axis and the Bloch oscillations along the SL axis become resonant with cyclotron rotation in the transverse plane. It is a phenomenon of considerable interest, so that it is important to understand the underlying mechanism. In an earlier Letter (Phys. Rev. Lett. 114, 166802 (2015)) we showed that, contrary to a general belief that drift enhancement occurs through chaotic diffusion along a stochastic web (SW) within semiclassical collisionless dynamics, the phenomenon actually arises through a non-chaotic mechanism. In fact, any chaos that occurs tends to reduce the drift. We now provide fuller details, elucidating the mechanism in physical terms, and extending the investigation. In particular, we: (i) demonstrate that pronounced drift enhancement can still occur even in the complete absence of an SW; (ii) show that, where an SW does exist and its characteristic slow dynamics comes into play, it suppresses the drift enhancement even before strong chaos is manifested; (iii) generalize our theory for non-small temperature, showing that heating does not affect the enhancement mechanism and accounting for some earlier numerical observations; (iv) demonstrate that certain analytic results reported previously are incorrect; (v) provide an extended critical review of the subject and closely related issues; and (vi) discuss some challenging problems for the future., 28 pages (including a detailed Contents, for convenience), 12 figures (some of them use postscript files of a reduced size: figures by the full-size files can be seen in the journal version)

The applicability of machine learning for predicting chaotic dynamics relies heavily upon the data used in the training stage. Chaotic time series obtained by numerically solving ordinary differential equations embed a complicated noise of the applied numerical scheme. Such a dependence of the solution on the numeric scheme leads to an inadequate representation of the real chaotic system. A stochastic approach for generating training times series and characterising their predictability is suggested to address this problem. The approach is applied for analysing two chaotic systems with known properties, Lorenz system and Anishchenko-Astakhov generator. Additionally, the approach is extended to critically assess a reservoir computing model used for chaotic time series prediction. Limitations of reservoir computing for surrogate modelling of chaotic systems are highlighted., Paper published as part of the special topic on In Memory of Vadim S. Anishchenko. Dataset used for figures and some additional comments on the used numerical methods are openly available in http://wrap.warwick.ac.uk/153069/

Ion channel selectivity is essential for their function, yet the molecular basis of a channel's ability to select between ions is still rather controversial. In this work, using a combination of molecular dynamics simulations and electrophysiological current measurements we analyze the ability of the NaChBac channel to discriminate between calcium and sodium. Our simulations show that a single calcium ion can access the Selectivity Filter (SF) interacting so strongly with the glutamate ring so as to remain blocked inside. This is consistent with the tiny calcium currents recorded in our patch-clamp experiments. Two reasons explain this scenario. The first is the higher free energy of ion/SF binding of Ca(2+) with respect to Na(+). The second is the strong electrostatic repulsion exerted by the resident ion that turns back a second potentially incoming Ca(2+), preventing the knock-on permeation mechanism. Finally, we analyzed the possibility of the Anomalous Mole Fraction Effect (AMFE), i.e. the ability of micromolar Ca(2+) concentrations to block Na(+) currents. Current measurements in Na(+)/Ca(2+) mixed solutions excluded the AMFE, in agreement with metadynamics simulations showing the ability of a sodium ion to by-pass and partially displace the resident calcium. Our work supports a new scenario for Na(+)/Ca(2+) selectivity in the bacterial sodium channel, challenging the traditional notion of an exclusion mechanism strictly confining Ca(2+) ions outside the channel.

Mechanical resonators are widely used as precision clocks and sensitive detectors that rely on the stability of their eigenfrequencies. The phase noise is determined by different factors including thermal noise, frequency noise of the resonator and noise in the feedback circuitry. Increasing the vibration amplitude can mitigate some of these effects but the improvements are limited by nonlinearities that are particularly strong for miniaturized micro- and nano-mechanical systems. Here we design a micromechanical resonator with non-monotonic dependence of the eigenfrequency on energy. Near the extremum, where the dispersion of the eigenfrequency is zero, the system regains certain characteristics of a linear resonator, albeit at large amplitudes. The spectral peak undergoes narrowing when the noise intensity is increased. With the resonator serving as the frequency-selecting element in a feedback loop, the phase noise at the extremum amplitude is ~3 times smaller than the minimal noise in the conventional nonlinear regime., Designing miniaturized oscillators with stable frequencies is challenging due to nonlinearities. Here, the authors demonstrate reduced phase noise using zero dispersion phenomena in a micromechanical resonator designed with non-monotonic dependence of the frequency of eigenoscillations on energy.

We analyze selective ionic conduction through an artificial nanopore in a single graphene sheet, using molecular dynamics simulations and the prehistory probability distribution. We assess position-dependent changes in the number and orientation of water molecules in the first and second hydration shells of the ion as it crosses the nanopore. We reveal coupling between an ionic double layer near the sheet to the statistical properties of the hydration shells.

Aeroelastic energy harvesters are a promising technology for powering wireless sensors and microelectromechanical systems. In this letter, we present a harvester inspired by the trembling of aspen leaves in barely noticeable winds. The galloping energy harvester, a curved blade oriented perpendicular to the flow, is capable of producing self-sustained oscillations at uncharacteristically low wind speeds. The dynamics of the harvesting system are studied experimentally and compared to a lumped parameter model. Numerical simulations quantitatively describe the experimentally observed dynamic behaviour. Flow visualisation is performed to investigate the patterns generated by the device. Dissimilar to many other galloping harvester designs, the flow is found to be attached at the rear surface of the blade when the blade is close to its zero displacement position, hence acting more closely to aerofoils rather than to conventionally used bluff bodies. Simulations of the device combined with a piezoelectric harvesting mechanism predict higher power output than that of a device with the square prism.

We study the highly-concerted motion of ions in anarrow biological ion channel (KcsA) by considering the notionof a quasiparticle, with specific focus on the transition process.Namely, we show that the ion entering or exiting the channelis correlated with the position of the quasiparticle. This resultis of importance in the rate theories of ion conduction throughnarrow channels and artificial nanopores.

Nonlinearity is ubiquitous in both natural and engineering systems. The resultant dynamics has emerged as a multidisciplinary field that has been very extensively investigated, due partly to the potential occurrence of nonlinear phenomena in all branches of sciences, engineering and medicine. Driving nonlinear systems with external excitations can yield a plethora of intriguing and important phenomena—one of the most prominent being that of resonance. In the presence of additional harmonic or stochastic excitation, two exotic forms of resonance can arise: vibrational resonance or stochastic resonance, respectively. Several promising state-of-the-art technologies that were not covered in part 2 of this theme issue are discussed here. They include inter alia the improvement of image quality, the design of machines and devices that exert vibrations on materials, the harvesting of energy from various forms of ambient vibration and control of aerodynamic instabilities. They form an important part of the theme issue as a whole, which is dedicated to an overview of vibrational and stochastic resonances in driven nonlinear systems. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 2)’.

With growing demand for small autonomous electrical devices, such as those in wireless sensor networks, energy harvesting has attracted interest with the promise of low maintenance and sustainable power sources. Galloping energy harvesters utilise the fluid-structure interaction to transform kinetic energy in fluid flow into electrical energy. The performance of galloping energy harvesters depends on the geometry of the tip, with the structure of the flow around the tip defining the nature of fluid-structure interaction and hence the potential efficiency of the device. In this work the curved blade tip geometry is investigated. To experimentally characterise the performance of the harvester, a method utilising the free oscillation transient is developed. The method avoids implementation of a transduction mechanism and hence optimisation of the associated parameters. The developed method is generic and can be applied to other energy generators. The power coefficient of curved blades of different curvatures is measured and the optimal range identified. The maximum coefficient of performance of the curved blade harvester occurs at tip speed ratios from 0.32 to 0.74 and reaches 0.08 , which is 3 to 4 times lower than Savonius turbines, the best performing devices at similar Reynolds numbers. The square prism geometry is used as a comparator and found to have a coefficient of performance 10 times less than the curved blade. Flow visualisations confirm the curved blade to act as an airfoil in the highest performing cases, hence future tip shapes should be developed to promote flow attachment.

A comparative analysis is made of various methods for processing electrocardiograms and RR-interval sequences. This analysis was carried out by using standard nonlinear-dynamics algorithms and methods. Apart from that, we assessed the expediency of using a number of characteristics to classify the cardiovascular system's state under stress.

Molecular dynamics simulations is an important tool for understanding the function-structure relationship in biological macro-molecules. To link different time scales in the simulations and consider rare events in macro-molecules, different techniques introducing constant biasing forces are applied. For potassium KscA ion channel the application of standard biased techniques leads to inconsistent results. A novel fluctuational approach which utilizes the duality of Hamiltonian formalism between the theory of optimal control and the theory of most probable fluctuations is suggested here. The transition of an ion between two sites of the KcsA channel is considered by using the novel approach, and the barrier between the two sites is evaluated. This approach can be applied to other channels, for example to sodium ion channels, but it would require further modifications.

Energy harvesting of ambient energy of different forms has attracted considerable attention of researchers from both theoretical and applied fields. Whereas a typical design of energy harvester is based on a resonant structure — a linear oscillator — aimed at a harmonic excitation, in practice the behaviour of a harvester deviates from linear, and ambient excitations have a much more complex structure than a simple sine-wave. Therefore, it is important to develop a framework for a nonlinear harvester design that would target the stochastic nature of vibrations for effective energy harvesting. In this paper such framework is based on stochastic frequency response. Using the suggested framework the performance of a harvester model for soft and hard nonlinearities in stiffness was compared with the linear harvester. The comparison indicates the presence of a novel phenomena linked to stochastic bifurcations observed by varying characteristics of harmonic noise.

NaChBac was the first discovered bacterial sodium voltage-dependent channel, yet computational studies are still limited due to the lack of a crystal structure. In this work, a pore-only construct built using the NavMs template was investigated using unbiased molecular dynamics and metadynamics. The potential of mean force (PMF) from the unbiased run features four minima, three of which correspond to sites IN, CEN, and HFS discovered in NavAb. During the run, the selectivity filter (SF) is spontaneously occupied by two ions, and frequent access of a third one is often observed. In the innermost sites IN and CEN, Na+ is fully hydrated by six water molecules and occupies an on-axis position. In site HFS sodium interacts with a glutamate and a serine from the same subunit and is forced to adopt an off-axis placement. Metadynamics simulations biasing one and two ions show an energy barrier in the SF that prevents single-ion permeation. An analysis of the permeation mechanism was performed both computing minimum energy paths in the axial–axial PMF and through a combination of Markov state modeling and transition path theory. Both approaches reveal a knock-on mechanism involving at least two but possibly three ions. The currents predicted from the unbiased simulation using linear response theory are in excellent agreement with single-channel patch-clamp recordings.

The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic solution. A new approach to the derivation of a Brownian dynamics (BD) model of ion permeation through the filter is discussed, based on unbiased MD simulations. It is shown that depending on additional assumptions, ion's dynamics can be described either by under-damped Langevin equation with constant damping and white noise or by Langevin equation with a fractional memory kernel. A comparison of the potential of the mean force derived from unbiased MD simulations with the potential produced by the umbrella sampling method demonstrates significant differences in these potentials. The origin of these differences is an open question that requires further clarifications., to appear in Eur. Phys. J. Spec. Top

Sensory cells usually transmit information to afferent neurons via chemical synapses, in which the level of noise is dependent on an applied stimulus. Taking into account such dependence, we model a sensory system as an array of LIF neurons with a common signal. We show that information transmission is enhanced by a nonzero level of noise. Moreover, we demonstrate a phenomenon similar to suprathreshold stochastic resonance with additive noise. We remark that many properties of information transmission found for the LIF neurons was predicted by us before with simple binary units [Phys. Rev. E 75, 021121 (2007)]. This confirmation of our predictions allows us to point out identical roots of the phenomena found in the simple threshold systems and more complex LIF neurons.

The activation dynamics of one-dimensional maps is considered. It is shown that the activation law describing the average time required for attaining a given boundary has the form of the error function (erfc), whereas approximation using the exponential law gives much worse results. In addition, it is demonstrated that linear analysis can be applied to a substantially nonlinear problem.

Noise-induced escape from the basin of attraction of a quasi-hyperbolic chaotic attractor in the Lorenz system is considered. The investigation is carried out in terms of the theory of large fluctuations by experimentally analyzing the escape prehistory. The optimal escape trajectory is shown to be unique and determined by the saddle-point manifolds of the Lorenz system. We established that the escape process consists of three stages and that noise plays a fundamentally different role at each of these stages. The dynamics of fluctuational escape from a quasi-hyperbolic attractor is shown to differ fundamentally from the dynamics of escape from a nonhyperbolic attractor considered previously [1]. We discuss the possibility of analytically describing large noise-induced deviations from a quasi-hyperbolic chaotic attractor and outline the range of outstanding problems in this field.

The energy-optimal migration of a chaotic oscillator from one attractor to another coexisting attractor is investigated via an analogy between the Hamiltonian theory of fluctuations and Hamiltonian formulation of the control problem. We demonstrate both on physical grounds and rigorously that the Wentzel–Freidlin Hamiltonian arising in the analysis of fluctuations is equivalent to Pontryagin's Hamiltonian in the control problem with an additive linear unrestricted control. The deterministic optimal control function is identified with the optimal fluctuational force. Numerical and analogue experiments undertaken to verify these ideas demonstrate that, in the limit of small noise intensity, fluctuational escape from the chaotic attractor occurs via a unique (optimal) path corresponding to a unique (optimal) fluctuational force. Initial conditions on the chaotic attractor are identified. The solution of the boundary value control problem for the Pontryagin Hamiltonian is found numerically. It is shown that this solution is approximated very accurately by the optimal fluctuational force found using statistical analysis of the escape trajectories. A second series of numerical experiments on the deterministic system (i.e. in the absence of noise) show that a control function of precisely the same shape and magnitude is indeed able to instigate escape. It is demonstrated that this control function minimizes the cost functional and the corresponding energy is found to be smaller than that obtained with some earlier adaptive control algorithms.

We address the enhancement of electron drift in semiconductor superlattices of nanometre scale that occurs in combined electric and tilted magnetic fields if Bloch oscillations become resonant with cyclotron rotation in the transverse plane. We uncover the true dynamical mechanism of the phenomenon: the electron dynamics at relevant time-scales is regular or almost regular, contrary to the widespread belief that the enhancement arises through chaotic diffusion between collisions. The theory provides an accurate description of earlier numerical simulations, predicts new remarkable features verified by simulations, and suggests new ways of controlling resonant transport., Comment: 6 pages of the main Letter and 23 pages of the Supplementary Material

A theoretical approach for characterizing the influence of asymmetry of noise distribution on the escape rate\ud of a multistable system is presented. This was carried out via the estimation of an action, which is defined as\ud an exponential factor in the escape rate, and discussed in the context of full counting statistics paradigm. The\ud approach takes into account all cumulants of the noise distribution and demonstrates an excellent agreement with\ud the results of numerical simulations. An approximation of the third-order cumulant was shown to have limitations\ud on the range of dynamic stochastic system parameters. The applicability of the theoretical approaches developed\ud so far is discussed for an adequate characterization of the escape rate measured in experiments.

A comparative analysis is made of various methods for processing electrocardiograms and RR-interval sequences. This analysis was carried out by using standard nonlinear-dynamics algorithms and methods. Apart from that, we assessed the expediency of using a number of characteristics to classify the cardiovascular system's state under stress.

The dynamical response of an underdamped Duffing oscillator to a quasiperiodic force is investigated in the presence and absence of very weak additive noise. Particular attention is focused on the effect of noise on the characteristics of strange nonchaotic attractors (SNAs). It is concluded that even extremely weak noise is sufficient to induce dynamical complexity in an SNA.

We study synchronization of switching processes in stochastic and chaotic bistable systems driven by a periodic signal in terms of phase synchronization. By introduction of instantaneous phases of transitions between metastable states and of the periodic forcing we show explicitly the effect of phase locking. The dynamics of phase difference appears to be qualitatively equivalent to that of a synchronized classical self-sustained oscillator. We have found that the degree of phase coherence between the input signal and the response estimated employing the effective diffusion constant is maximal at an optimal noise level in a stochastic bistable system or at an optimal value of a control parameter in a purely deterministic case. We also consider the effect of mutual synchronization of the switching processes in coupled stochastic and chaotic bistable systems.

Noise-induced escape from the basin of attraction of a strange attractor (SA) in a periodically excited nonlinear oscillator is investigated. It is shown by numerical simulation methods that escape occurs in two steps: transfer of the system from the SA to a close-lying saddle cycle along several optimal trajectories, and a subsequent fluctuation-induced transfer from the basin of attraction of the SA along a single optimal trajectory. The possibility of using the results of this work to solve problems of the optimal control of switchings from an attractor and for constructing theoretical estimates of the escape probability is discussed.

Synchronization of two symmetrically coupled Lorenz systems, each of them considered a chaotic bistable system, is investigated numerically. A phenomenon of synchronization of the mean frequencies of switchings in coupled chaotic bistable systems is found. Bifurcations taking place in the system are analyzed. It is shown that there is the region on the ``coupling-detuning'' parameter plane where the mean frequencies of switchings coincide with a certain accuracy.

We discuss an example of self-organisation in a biological system. It arises from long-range ion-ion interactions, and it leads us to propose a novel mechanism of enhanced conduction in ion channels. The underlying mechanism involves charge fluctuations near the channel mouth, amplified by the mismatch between the relative permittivities of water and the protein of the channel walls. We use Brownian dynamics simulations to show that, as in conventional ``knock-on'' permeation, these interactions can strongly enhance the channel current; but unlike the conventional mechanism the enhancement occurs without the instigating bath ion entering the channel. The transition between these two mechanisms is clearly demonstrated, emphasizing their distinction. A simple model accurately reproduces the observed phenomena. We point out that electrolyte plus protein of low relative permittivity are universal in living systems, so that long-range ion-ion correlations of the kind considered must be common.

Continuous glucose monitoring is increasingly used in the management of diabetes. Subcutaneous glucose profiles are characterised by a strong non-stationarity, which limits the application of correlation-spectral analysis. We derived an index of linear predictability by calculating the autocorrelation function of time series increments and applied detrended fluctuation analysis to assess the non-stationarity of the profiles. Time series from volunteers with both type 1 and type 2 diabetes and from control subjects were analysed. The results suggest that in control subjects, blood glucose variation is relatively uncorrelated, and this variation could be modelled as a random walk with no retention of 'memory' of previous values. In diabetes, variation is both greater and smoother, with retention of inter-dependence between neighbouring values. Essential components for adequate longer term prediction were identified via a decomposition of time series into a slow trend and responses to external stimuli. Implications for diabetes management are discussed. © 2012 Elsevier Ireland Ltd.

Brownian dynamics simulations provide evidence for a remote knock-on mechanism facilitating the permeation of a biological ion channel by an ion that is initially trapped at the selectivity filter (SF). Unlike the case of conventional direct knock-on, the second ion that instigates permeation does not need to enter the channel. Nor does it necessarily take the place of the permeating ion at the SF, and it can even be of a different ionic species. The study is based on the simultaneous, self-consistent, solution of the coupled Poisson and Langevin equations for a simple generic model, taking account of all the charges present. The new permeation mechanism involves electrostatic amplification attributable to the permittivity mismatch between water and protein: the arrival of the instigating ion at the channel entrance reduces the exit barrier for the ion trapped at the SF, facilitating escape.

We consider the stochastic dynamics of escape in an excitable system, the FitzHugh-Nagumo (FHN) neuronal model, for different classes of excitability. We discuss, first, the threshold structure of the FHN model as an example of a system without a saddle state. We then develop a nonlinear (nonlocal) stability approach based on the theory of large fluctuations, including a finite-noise correction, to describe noise-induced escape in the excitable regime. We show that the threshold structure is revealed via patterns of most probable (optimal) fluctuational paths. The approach allows us to estimate the escape rate and the exit location distribution. We compare the responses of a monostable resonator and monostable integrator to stochastic input signals and to a mixture of periodic and stochastic stimuli. Unlike the commonly used local analysis of the stable state, our nonlocal approach based on optimal paths yields results that are in good agreement with direct numerical simulations of the Langevin equation. DOI: 10.1103/PhysRevE.87.032116

We have studied the influence of uncorrelated Gaussian fluctuations on the propagation of pulses in an excitable medium modeled by the FitzHugh-Nagumo system under an external point action. Depending on the properties of this medium, one of the two possible scenarios is realized in the noise-induced suppression of propagating pulses. The first scenario can be classified as the noise-induced incoherence (breakage of the links) between adjacent elements of the medium. The second scenario is related to a spontaneous generation of pulses in the medium under the action of fluctuations. These models are applied to analysis of some recent biological experiments devoted to the dynamics of calcium waves.

We review an approach to separatrix chaos that has allowed us to solve some significant problems by: (i) finding analytically the maximum width of the chaotic layer, a problem that lay unsolved for 40 years, and showing that the maximum may be much larger than had previously been assumed; (ii) describing the drastic facilitation of the onset of global chaos between neighboring separatrices, a phenomenon discovered eight years ago.

We consider time-periodically perturbed 1D Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small or moderate ranges: this corresponds to the involvement of resonance dynamics into the separatrix chaos. We develop a method matching the discrete chaotic dynamics of the separatrix map and the continuous regular dynamics of the resonance Hamiltonian. The method has allowed us to solve the long-standing problem of an accurate description of the maximum of the separatrix chaotic layer width as a function of the perturbation frequency. It has also allowed us to predict and describe new phenomena including, in particular: (i) a drastic facilitation of the onset of global chaos between neighbouring separatrices, and (ii) a huge increase in the size of the low-dimensional stochastic web.

The dynamics of a quasiperiodic map is analyzed both in the presence and in the absence of weak noise. It is shown that, in the presence of weak noise, a strange chaotic attractor with a negative Lyapunov exponent and sensitive dependence of trajectories on the initial conditions can exist in the system. This means that the types of motion of a fluctuating system cannot be classified only by the sign of the leading Lyapunov exponent.

Stochastic webs were discovered, first by Arnold for multi-dimensional Hamiltonian systems, and later by Chernikov et al. for the low-dimensional case. Generated by weak perturbations, they consist of thread-like regions of chaotic dynamics in phase space. Their importance is that, in principle, they enable transport from small energies to high energies. In this introductory review, we concentrate on low-dimensional stochastic webs and on their applications to quantum transport in semiconductor superlattices subject to electric and magnetic fields. We also describe a recently-suggested modification of the stochastic web to enhance chaotic transport through it and we discuss its possible applications to superlattices. keywords: stochastic webs; quantum transport; superlattices; separatrix chaos, Review, to be published in "Contemporary Physics"

The problem of how to reconstruct the parameters of a stochastic nonlinear dynamical system when these are time-varying is considered in the context of online decoding of physiological information from neuron signaling activity. To model the spiking of neurons, a set of FitzHugh-Nagumo (FHN) oscillators is used. It is assumed that only a fast dynamical variable can be detected for each neuron, and that the monitored signals are mixed by an unknown measurement matrix. The Bayesian framework introduced in Paper I (Phys. Rev. E 77, 06110500 (2008)) is applied both for reconstruction of the model parameters and elements of the measurement matrix, and for inference of the time-varying parameters in the non-stationary system. It is shown that the proposed approach is able to reconstruct unmeasured (hidden) slow variables of the FHN oscillators, to learn to model each individual neuron, and to track continuous, random and step-wise variations of the control parameter for each neuron in real time.

Recent progress towards an understanding of fluctuational escape from chaotic attractors (CAs) is reviewed and discussed in the contexts of both continuous systems and maps. It is shown that, like the simpler case of escape from a regular attractor, a unique most probable escape path (MPEP) is followed from a CA to the boundary of its basin of attraction. This remains true even where the boundary structure is fractal. The importance of the boundary conditions on the attractor is emphasized. It seems that a generic feature of the escape path is that it passes via certain unstable periodic orbits. The problems still remaining to be solved are identified and considered.

The nonlinear transformation of an external noisy signal by an array of noninteracting elements with internal noise is considered. The array simulates a neuronal system that processes spike trains. It is shown that increasing the number of array elements entails significant extending of the stochastic synchronization region and improvement of the signal-to-noise ratio (SNR). The effects are demonstrated for arrays of triggers, overdamped bistable oscillators, and Fitzhugh-Nagumo systems. The interrelation between SNR improvement and the efficiency of information processing is discussed.