Igor A Khovanov

• PhD
• Professor (Associate) at University of Warwick

We use all-atom molecular dynamics simulations to investigate ionic conduction in a short, charged, single-wall carbon nanotube. They reveal ionic Coulomb blockade (ICB) oscillations in the current as a function of the fixed charge on the wall, and an associated occupancy staircase. Current peaks related to fluctuations around the 2 → 1 and 1 → 0 s...

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 th...

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 r...

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 frequen...

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 r...

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...

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 frequen...

Nonlinear systems are abundant in nature. Their dynamics have been investigated very extensively, motivated partly by their multidisciplinary applicability, ranging from all branches of physical and mathematical sciences through engineering to the life sciences and medicine. When driven by external forces, nonlinear systems can exhibit a plethora o...

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 in...

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...

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 be...

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...

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 t...

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 t...

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 ranging from thermal noise and frequency noise of the resonator to noise in the feedback circuitry. Increasing the vibration amplitude can mitigate some of these e...

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 effect...

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 experimen...

Noise is universal and multi-faceted. In everyday life, the aspects we encounter tend to be annoying, for example, loud conversations when we wish to enjoy a quiet cup of tea, or students chatting during a lecture. But acoustic noise can sometimes be useful e.g. when it indicates that the kettle is boiling, as an essential prelude to the tea, or wh...

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-sustai...

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...

A key driving force for ion channel selectivity is represented by the negative charge of the Selectivity Filter carried by aspartate (D) and glutamate (E) residues. However, the structural effects and specific properties of D and E residues have not been extensively studied. In order to investigate this issue we studied the mutants of NaChBac chann...

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...

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.

NaChBac was the first discovered 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...

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...

The efficiency of linear and nonlinear harvesters with different types of nonlinearity is compared. Narrow band ambient vibrations are modeled by harmonic Gaussian noise. We show that the performance of nonlinear harvesters strongly depends on both the form of nonlinearity and the properties of the noise. Particular forms of nonlinearities which ca...

A theoretical approach for characterizing the influence of asymmetry of noise distribution on the escape rate of a multistable system is presented. This was carried out via the estimation of an action, which is defined as an exponential factor in the escape rate, and discussed in the context of full counting statistics paradigm. The approach takes...

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e discuss an example of self-organization in a biological system. It arises from long-range ion–ion interactions, and it leads us to propose a new kind 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 p...

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 filte...

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 necessar...

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 fl...

We present and discuss a modified version of reaction rate theory (RRT) to describe the passage of a positive ion through a biological ion channel. It takes explicit account of the non-equilibrium nature of the permeation process. Unlike traditional RRT, it allows for the non-constant transition rates that arise naturally in an archetypal model of...

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...

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 glo...

Design of an efficient energy harvester is now feasible as technology develops and a viable approach to solve this need is to exploit the concept and application of a nonlinear design. In this letter, we conducted a comparative analysis of linear and nonlinear piezoelectric energy harvesting from random impulsive excitations modelled by white Poiss...

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 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 appear...

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 dev...

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 ene...

We consider an archetypal example of a low‐dimensional stochastic web, arising in a 1D oscillator driven by a plane wave of a frequency equal or close to a multiple of the oscillator’s natural frequency. We show that the web can be greatly enlarged by the introduction of a slow, very weak, modulation of the wave angle. Generalizations are discussed...

We discuss open problems related to the stochastic modeling of cardiac function. The work is based on an experimental investigation of the dynamics of heart rate variability (HRV) in the absence of respiratory perturbations. We consider first the cardiac control system on short time scales via an analysis of HRV within the framework of a random wal...

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 attr...

The problem of how to reconstruct the parameters of a stochastic nonlinear dynamical system when they 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 dynami...

The response of a weakly damped bistable oscillator to an external periodic force is considered theoretically. In the approximation of weak signals we can write a linearized equation for the signal and the corresponding nonlinear equation for the noise. These equations contain two unknown parameters: An effective stiffness and an additional damping...

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 s...

We study the nonlinear response of a noisy bistable system to a biperiodic signal through experiments with an electronic circuit (Schmitt trigger). The signal we use is a biharmonic one, i.e., a superposition of low and high frequency harmonic components. It is shown that the mean switching frequency (MSF) of the system can be locked at both low an...

Continuous and pulsed forms of control of a multistable system are compared directly, both theoretically and numerically, taking as an example the switching of a periodically driven class-B laser between its stable and unstable pulsing regimes. It is shown that continuous control is the more energy efficient. This result is illuminated by making us...

A direct comparison between continuous and discrete forms of analysis of control and stability is investigated theoretically and numerically. We demonstrate that the continuous method provides a more energy-efficient means of controlling the switching of a periodically-driven class-B laser between its stable and unstable pulsing regimes. We provide...

Coupled nonlinear oscillators operating in the presence of noise are widespread in nature. Examples include brain waves and cardiovascular oscillations. They can be amplitude or frequency‐coupled, and are characterised by time‐varying frequencies of oscillation. The time series related to cardiovascular and brain oscillations have been extensively...

We report on the observation of coherence resonance for a semiconductor laser with short optical feedback close to Hopf bifurcations. Noise-induced self-pulsations are documented by distinct Lorentzian-like features in the power spectrum. The character of coherence is critically related to the type of the bifurcation. In the supercritical case, spe...

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 applie...

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 scen...

Double strategy of chaos and fluctuation controls is developed. Noise-induced failures in the stabilization of аn unstable orbit in the one-dimensional logistic mар are considered as large fluctuations from a stable state. The properties of the large fluctuations are examined by determination and analysis of the optimal path and the optimal fluctua...

Bispectral analysis, a technique based on high-order statistics, is extended to encompass time dependence for the case of coupled nonlinear oscillators. It is applicable to univariate as well as to multivariate data obtained, respectively, from one or more of the oscillators. It is demonstrated for a generic model of interacting systems whose basic...

Noise-induced failures in the stabilization of an unstable orbit in the one-dimensional logistic map are considered as large fluctuations from a stable state. The properties of the large fluctuations are examined by determination and analysis of the optimal path and the optimal fluctuational force corresponding to the stabilization failure. The pro...

Fluctuational transitions between two coexisting attractors are investigated. Two different systems are considered: the periodically driven nonlinear oscillator and the two-dimensional map introduced by Holmes. These two systems have smooth and fractal boundaries, respectively, separating their coexisting attractors. It is shown that, starting from...

We discuss the gain in signal-to-noise ratio (SNR) recently reported by Liu et al. [Phys. Rev. E 63, 051912 (2001)] in the Hodgkin-Huxley neuronal model. We show first that the possibility of signal-to-noise ratio enhancements can be checked by consideration of the statistical characteristics of switching between the system states, and we examine h...

Noise-induced failures in the stabilization of an unstable orbit in the one-dimensional logistic map are considered as large fluctuations from a stable state. The properties of the large fluctuations are examined by determination and analysis of the optimal path and the optimal fluctuational force corresponding to the stabilization failure. The pro...

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 manifold...

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...

Saddle cycles play an important role in solving the problem of controlling complex dynamics in optical systems. Therefore studying the influence of noise on the structure and properties of saddle cycles is actual task. In the paper, the pointwise dimension of saddles cycles for different types of chaotic attractors is considered in the presence and...

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.

Noise-induced escape from a quasi-hyperbolic attractor in the Lorenz system is investigated via an analysis of the distributions of both the escape trajectories and the corresponding realizations of the random force. It is shown that a unique escape path exists, and that it consists of three parts with noise playing a different role in each. It is...

In this chapter the authors discuss the application of simulation techniques to the study of fluctuational escape and related phenomena in nonliner optical systems: that is, situations where a large deviation of the system from an equilibrium state occurs under the influence of relatively weak noise present in the system. The authors are interested...

The energy-optimal entraining of the dynamics of a periodically driven oscillator, moving it from a chaotic attractor to a coexisting stable limit cycle, is investigated via analysis of fluctuational transitions between the two states. The deterministic optimal control function is identified with the corresponding optimal fluctuational force, which...

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 flu...

Fluctuational transitions between the stationary states of periodically-driven nonlinear oscillators are investigated by means of numerical simulations and analogue experiments for over-damped, weakly damped and chaotic motion. It is shown that transitions take place along distinct most probable escape paths (MPEPs) in all three cases. The transiti...

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 dy...

The problem of activated escape in a far-from-equilibrium system is analyzed theoretically, numerically and by analogue electronic experiments. The process is shown to occur via optimal fluctuations that are well described, under diverse conditions, in terms of a new physical quantity, the logarithmic susceptibility (LS). .

Noise-induced escape from a quasi-attractor, and from the Lorenz attractor with non-fractal boundaries, are compared through measurements of optimal paths. It has been found that, for both types of attractor, there exists a most probable (optimal) escape trajectory, the prehistory of the escape being defined by the structure of the chaotic attracto...

Noise-induced transitions between coexisting stable states of a periodically driven nonlinear oscillator have been investigated by means of analog experiments and numerical simulations in the non-adiabatic limit for a wide range of oscillator parameters. It is shown that, for over-damped motion, the field-induced corrections to the activation energ...

The dynamical properties of the quasiperiodic logistic map with and without a very weak noise are compared, and the influence of noise on its strange nonchaotic attractor (SNA) is investigated. It is found that, in the presence of weak noise, the largest Lyapunov exponent gives misleading information about the dynamical properties of the attractor....

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-i...

We study synchronization of switching processes in stochastic and chaotic bistable the systems driven by а periodic signal in terms of phase synchronization. Introducing instantaneous phases of transitions between metastable states and the periodic forcing we show explicitly the effect of phase locking. The dynamics of phase difference арреагs to b...

The dynamics of two symmetrically coupled Lorenz systems is investigated by means of a numerical experiment. A bifurcation analysis of the synchronization process is presented. The results are compared with numerical experiments. It is shown that changing the coupling can synchronize or desynchronize the subsystems.

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...

Synchronization of two symmetrically coupled Lorenz systems, each of them being considered as a chaotic bistable system, is investigated numerically. A new phenomenon of synchronization of switching processes in coupled chaotic bistable systems is found. It is shown that there is the region on the “coupling-detuning” parameter plane where the mean...

We discuss the peculiarities of stochastic resonance in a bistable system for different levels of the amplitude of a regular force. It is shown that for a certain class of signals the output signal-to-noise ratio, as conventionally defined, can substantially exceed the signal-to-noise ratio at the input. The connection between the phenomenon of swi...

A numerical analysis is made of the synchronization of the mean switching frequencies in two symmetrically coupled Lorenz systems functioning in a chaotic regime. The observed effect on the coupling-mismatch parameter plane corresponds to a region of synchronization of the switching processes, within which the mean switching frequencies coincide to...

The phenomenon of stochastic resonance in a bistable system modeling overdamped oscillator is studied by numerical simulations and experiments. Experimental data are compared with theoretical results. Stochastic resonance in Chua’s circuit is investigated in detail for different regimes of its own dynamics. The main characteristics of stochastic re...

A technique is studied for increase of amplifier sensitivity using the method of noise nonlinear filtering by a bistable system in the stochastic resonance regime. Noise figure decrease is investigated for a filter with bistable symmetrical potential. Experimental check of the effect has been carried out at the frequency 400 Hz. The results of theo...