Impulse Perturbations Research Articles

Asymptotic Dissipativity for Merged Stochastic Evolutionary Systems with Markov Switchings and Impulse Perturbations under Conditions of Lévy Approximation

Conditions for asymptotic dissipativity are established for the merged system of stochastic differential equations with Markov switchings and impulse perturbations under conditions of Levy approximation. In particular, it is analyzed how the behavior of the boundary process depends on the pre-limiting normalization of a stochastic evolution system in the ergodic Markovian environment under the conditions of Levy approximation.

Asymptotic Properties of the Impulse Perturbation Process under the Poisson Approximation Conditions with the Equilibrium Point of Quality Criterion

For a system of stochastic differential equations with Markov switchings and impulse perturbation under the Poisson approximation scheme and the conditions of the existence of a single equilibrium point of the quality criterion, the limit generators for the impulse process and the dynamic system are constructed. The complexity of the proposed evolutionary model lies in its three properties. First, the system is under conditions of an external random effect, which is modeled using the Markov switching process. Processes with independent increments, which also depend on the Markov switching process, have certain characteristics between the moments of its restoration, and at the moments of restoration, these characteristics change. Therefore, the so-called "gluing" of trajectories of processes with independent increments occurs. Second, the model contains a Poisson approximation scheme, which is a generalization of the classical averaging scheme and is determined by normalization depending on a small parameter. In the classical approximation scheme in the limit process, we do not see large jumps in the system. The maximum that we get is the shift of the deterministic trajectory. However in the Poisson approximation scheme, which was invented by Korolyuk and Limnios in the monograph of 2005, this problem is eliminated, therefore, both a deterministic shift and large jumps will take place in the limit. Third, the system has a control function, which is determined using the Robins-Monroe stochastic approximation procedure. This procedure solves the problem of determination of the equilibrium point of the regression function and consists in finding the unique solution to the equation relative to control. Assuming the existence of a unique control on every interval, we solve a two-level problem. The question, how the behavior of the limit process depends on the prelimit normalization of the stochastic system in an ergodic Markov environment is studied in the article.

Research on Synchronous Control Method for Suppressing Nonlinear Impulse Perturbation of Photovoltaic Grid-Connected Inverter

In this paper, the synchronous control problem of photovoltaic grid-connected inverter with nonlinear impulse perturbation is studied. The mathematical model of photovoltaic grid-connected converter is established by using Kirchhoff’s law. The nonlinear impulse perturbation characteristics of grid-connected current are studied and analyzed. Controllers are designed to suppress nonlinear impulse perturbation. The effectiveness of the controller is verified by Lyapunov stability theory. Finally, the simulation design is carried out by simulink in Matlab and the test platform is constructed. In this paper, simulation verification and data comparison are carried out by using various control methods for suppressing nonlinear impulse perturbation of grid-connected currents. Compared with PI controller, PR controller and other controller, the output harmonic content of photovoltaic inverter can be controlled within 1%, which can effectively reduce the harmonic content. The power quality of grid-connected current is improved. The feasibility and effectiveness of the control strategy proposed are verified by simulation and experiments.

Artificial modulation-free Pound-Drever-Hall method for laser frequency stabilization.

We have proposed an artificial modulation-free Pound-Drever-Hall (PDH) method for laser frequency stabilization and demonstrated it via two-color polarization spectroscopy of Rydberg electromagnetically induced transparency (EIT) resonance in a room-temperature rubidium vapor. Due to the unique error signal profile, the conventional PDH method owns a large capture range in laser frequency locking. Here we manually construct a PDH error signal via a linear combination of polarization spectroscopies of the Rydberg EIT resonances without and with a magnetic field applied. The artificial modulation-free PDH error signal owns a subnatural linewidth dispersion curve as well as a large capture range with which we successfully stabilize the laser to an absolute atomic frequency reference in a long running time, immune to environmental fluctuation and even manmade impulse perturbation. This method can provide an absolute frequency reference based on atomic transition while keeping similar locking ability to provide corrections for frequency fluctuations over a broad bandwidth as the conventional PDH.

Asymptotic properties of the impulse perturbation process under Levy approximation conditions

Asymptotic properties of the impulse perturbation process under Levy approximation conditions

Dynamic of a nonautonomous two-species impulsive competitive system with infinite delays

Abstract In this paper, we consider a nonautonomous two-species impulsive competitive system with infinite delays. By the impulsive comparison theorem and some mathematical analysis, we investigate the permanence, extinction and global attractivity of the system, as well as the influence of impulse perturbation on the dynamic behaviors of this system. For the logistic type impulsive equation with infinite delay, our results improve those of Xuxin Yang, Weibing Wang and Jianhua Shen [Permanence of a logistic type impulsive equation with infinite delay, Applied Mathematics Letters, 24(2011), 420-427]. For the corresponding nonautonomous two-species impulsive competitive system without delays, we discuss its permanence, extinction and global attractivity, which weaken and complement the results of Zhijun Liu and Qinglong Wang [An almost periodic competitive system subject to impulsive perturbations, Applied Mathematics and Computation, 231(2014), 377-385].

Virtual Cortical Stimulation Mapping of Epilepsy Networks to Localize the Epileptogenic Zone.

Cortical stimulation mapping (CSM) is a common clinical procedure for mapping eloquent cortex in epilepsy patients. Electrical responses to the stimulation, or after-discharges (ADs), that occur in response to stimulation can point to unstable regions of cortex that are more prone to spontaneous seizures. Clinicians are interested in identifying regions that start seizures, i.e., the epileptogenic zone (EZ), so that they can target treatment. However, during CSM, not all regions are stimulated, as it would be time-consuming and potentially harmful to the patient. This limits the clinician's ability to fully explore ADs to reliably localize the EZ. In this paper, we develop a virtual CSM procedure that processes pre-seizure intracranial EEG recordings obtained from epilepsy patients being treated at three different epilepsy centers. First, we identify a linear time varying network (LTVN) model from electrocorticography (ECoG) and stereo-EEG (SEEG) data using sparse least squares estimation for each patient. We then construct an virtual CSM by applying impulse perturbations to each electrode contact in the LTVN model and then measuring the ADs of the network. We summarize the l2-norm of the responses in the form of a heatmap that shows the spatio-temporal evolution of the ADs before, during, and after seizures. Finally we compute an impulse response ratio (IRR) metric from each heatmap, that measures the ratio between the mean norm of ADs of clinically annotated EZ contacts and the mean norm of ADs of the remaining contacts. We find that the IRR is higher in maps derived from patients with successful surgical outcomes and lower in failed surgical outcomes. This suggests that virtual CSM may provide valuable information to clinicians regarding EZ location.

Adequacy assessment of the simulation of construction machines’ dynamic transmission systems

In the study of vibroacoustic processes in mechanical gears of construction and road machines, one of their important tasks is to assess the compliance of the developed mathematical models with real objects. The article presents the methodology and theoretical dependencies for numerical methods for assessing the adequacy of the models of gears of mechanical transmissions of construction machines, which are linear oscillatory systems. The developed technique is based on the test effect of a single impulse perturbation on the model and the real object and comparing the spectra of their own oscillations. The results of theoretical and experimental studies of the primary shaft of a manual transmission of a medium-class earth-moving machinery are presented.

Selective Transient Cooling by Impulse Perturbations in a Simple Toy Model.

We show in a simple exactly solvable toy model that a properly designed impulse perturbation can transiently cool down low-energy degrees of freedom at the expense of high-energy ones that heat up. The model consists of two infinite-range quantum Ising models: one, the high-energy sector, with a transverse field much bigger than the other, the low-energy sector. The finite-duration perturbation is a spin exchange that couples the two Ising models with an oscillating coupling strength. We find a cooling of the low-energy sector that is optimized by the oscillation frequency in resonance with the spin exchange excitation. After the perturbation is turned off, the Ising model with a low transverse field can even develop a spontaneous symmetry breaking despite being initially above the critical temperature.

Multiplicity of chaotic attractors in a model of lasers with variable feedback delay

We demonstrate coexistence of chaotic attractors induced by periodic modulation of the delay time in the feedback circuit which controls pumping rate in a laser. Depending on the n-number of pulses in the delay interval, the dynamics of the pulse regime is described by the dynamics of the (2n + 2)-dimensional map. It is possible to switch chaotic regimes of different structures by a single impulse perturbation of pumping in a suitable phase of the oscillations.

Obtaining high-energy responses of nonlinear piezoelectric energy harvester by voltage impulse perturbations

Nonlinear energy harvesters have attracted wide research attentions to achieve broadband performances in recent years. Nonlinear structures have multiple solutions in certain frequency region that contains high-energy and low-energy orbits. It is effectively the frequency region of capturing a high-energy orbit that determines the broadband performance. Thus, maintaining large-amplitude high-energy-orbit oscillations is highly desired. In this paper, a voltage impulse perturbation approach based on negative resistance is applied to trigger high-energy-orbit responses of piezoelectric nonlinear energy harvesters. First, the mechanism of the voltage impulse perturbation and the implementation of the synthetic negative resistance circuit are discussed in detail. Subsequently, numerical simulation and experiment are conducted and the results demonstrate that the high-energy-orbit oscillations can be triggered by the voltage impulse perturbation method for both monostable and bistable configurations given various scenarios. It is revealed that the perturbation levels required to trigger and maintain high-energy-orbit oscillations are different for various excitation frequencies in the region where multiple solutions exist. The higher gain in voltage output when high-energy-orbit oscillations are captured is accompanied with the demand of a higher voltage impulse perturbation level.

Comparison of the Performances of Different Reduced Forms of a Condenser Model

AbstractSymbolic manipulation uncovers hidden constraints for a model and facilitates model reduction for solution. The present work points out possible pitfalls of this procedure and finds possible solutions. The performances of different reduced forms of a condenser model are compared under step and impulse perturbations. The system does not need to be at steady state before perturbation. Some symbolically manipulated models cause inconsistent reinitialization and convergence and introduce significant computational errors. Physically unreasonable system behavior thus emerges, which worsens with increasing model complexity. Nevertheless, the less symbolically manipulated models present realistic and accurate behaviors. Another approach to model reduction is the reformulation of a model through a physical insight. A physically reformulated model proposed for the system leads to accurate and physically reasonable system behavior.

Single-species model under seasonal succession alternating between Gompertz and Logistic growth and impulsive perturbations

This paper proposes a single species system under seasonal succession and impulsive perturbations. The system is composed of two processes: one governed by the Gompertz equation, and the other modelled by the Logistic equation. The two processes are connected by impulse perturbations. Some very general, weak criteria on the permanence, existence, uniqueness and global stability of the positive periodic solution are established by analysis approaches based on the theory of discrete dynamical systems. The theoretical results are demonstrated by special examples and numerical simulations.

Variability features associated with ozone column and surface UV irradiance observed over Svalbard from 2008 to 2014

The present report shortly summarises the conclusions about the ozone column and solar UV irradiance variability that were achieved through the analysis of the data obtained from the narrow-band filter radiometer UV-RAD, operating at Ny-Alesund from 2008 to 2014. The polar summer gives the opportunity to register the solar irradiance 24 h per day during several months that provides comparatively long continuous time series as regards for the short- (diurnal) and medium-term (monthly) variations. To exclude the hypothesis about the artificial nature of the large amplitudes registered in the short-term ozone column variations, which can be due to the measurement or methodological errors, they were related to the corresponding variations in the solar UV radiation. In addition, these oscillations were studied using the methods developed for the analysis of non-linear dynamical systems that revealed a complex chaotic interaction between the ozone column and five other atmospheric factors. This approach leads to the conclusion that the short-term variations can be predicted for 10–20 h if a long history is available. The effect of a sporadic phenomenon, such as the ozone depletion event, occurred over Arctic in the spring of 2011, which can be considered an impulse perturbation of the medium-term ozone variations, on the mid-latitude ozone column and surface solar UV irradiance has been studied by analysing the data collected from six surface stations.

Positive Periodic Solutions of a Neutral Impulsive Predator-Prey Model

We investigate a ratio-dependent predator-prey model with Holling type III functional response based on system of neutral impulsive differential equations. Sufficient conditions for existence of positive periodic solutions are obtained by applying continuation theorem. Our main results demonstrate that under the suitable periodic impulse perturbations, the neutral impulsive system preserves the periodicity of the corresponding neutral system without impulse. In addition, our results can be applied to the corresponding system without impulsive effect, and thus, extend previous results.

Modeling of elastic waves in a blocky medium based on equations of the Cosserat continuum

Based on the equations of the dynamics of piecewise-homogeneous elastic material, parallel computational algorithms are developed to simulate the process of stress and strain wave propagation in a medium consisting of a large number of blocks interacting through compliant interlayers. Computations of waves caused by localized impulse perturbations show that such a medium can be considered as isotropic only in the case of sufficiently thin interlayers. In the case of relatively thick interlayers, the anisotropy effects are observed which consist in the appearance of elongated wave fronts along the coordinate directions and characteristic oscillations of velocities and stresses because of the rotational motion of blocks. For the description of waves in a blocky medium with thin interlayers, the equations of the isotropic Cosserat continuum are applicable. As the thickness of interlayers increases, the orthotropic Cosserat continuum theory which takes into account the symmetry of elastic properties relative to the coordinate planes can be applied. By comparing the elastic wave velocities in the framework of piecewise-homogeneous model and continuum model, a simple method is obtained to estimate the mechanical parameters of the orthotropic Cosserat continuum modeling a blocky medium. In two-dimensional formulation of the orthotropic model the computational algorithm and the program system are worked out for the analysis of propagation of elastic waves. The comparison showed good qualitative agreement between the results of computations of waves caused by localized impulses, in the framework of the model of a blocky medium with compliant interlayers and the model of orthotropic Cosserat continuum.

On exponential stability of functional differential equations with variable impulse perturbations

We consider a class of functional differential equations subject to perturbations, which vary in time, and we study the exponential stability of solutions of these equations using the theory of generalized ordinary differential equations and Lyapunov functionals. We introduce the concept of variational exponential stability for generalized ordinary differential equations and we develop the theory in this direction by establishing conditions for the trivial solutions of generalized ordinary differential equations to be exponentially stable. Then, we apply the results to get corresponding ones for impulsive functional differential equations. We also present an example of a delay differential equation with Perron integrable right-hand side where we apply our result.

Excitable Signal Transduction Induces Both Spontaneous and Directional Cell Asymmetries in the Phosphatidylinositol Lipid Signaling System for Eukaryotic Chemotaxis

Intracellular asymmetry in the signaling network works as a compass to navigate eukaryotic chemotaxis in response to guidance cues. Although the compass variable can be derived from a self-organization dynamics, such as excitability, the responsible mechanism remains to be clarified. Here, we analyzed the spatiotemporal dynamics of the phosphatidylinositol 3,4,5-trisphosphate (PtdInsP3) pathway, which is crucial for chemotaxis. We show that spontaneous activation of PtdInsP3-enriched domains is generated by an intrinsic excitable system. Formation of the same signal domain could be triggered by various perturbations, such as short impulse perturbations that triggered the activation of intrinsic dynamics to form signal domains. We also observed the refractory behavior exhibited in typical excitable systems. We show that the chemotactic response of PtdInsP3 involves biasing the spontaneous excitation to orient the activation site toward the chemoattractant. Thus, this biased excitability embodies the compass variable that is responsible for both random cell migration and biased random walk. Our finding may explain how cells achieve high sensitivity to and robust coordination of the downstream activation that allows chemotactic behavior in the noisy environment outside and inside the cells.

PathPSA: A Dynamical Pathway-Based Parametric Sensitivity Analysis

Normal functioning of biological systems relies on coordinated activities of biomolecules participating in a complex network of biological interactions. As human intuition is often incapable in analyzing how biological functions emerge from such complex interactions, the use of mathematical models and systems analysis tools has become critical in understanding biological system behavior. While biological functions have been associated with the connectivity (structure) and pathways of the network and the kinetics of the processes involved, most model analyses address each of these aspects separately. In contrast, we present a novel sensitivity analysis, called pathway-based parametric sensitivity analysis (pathPSA), which combines the analysis of both network structure and kinetics. Unlike existing sensitivity analyses, pathPSA relies on perturbing the kinetics of pathways in the network, using persistent perturbations or impulse perturbations at varying time. Consequently, the sensitivity coefficients can give insights on the dominant pathways in a network and any transient shift in the rate controlling mechanism. The efficacy of pathPSA is demonstrated through an application to understand competing signaling pathways in programmed cell death network.

Dynamic Behaviors of Holling Type II Predator-Prey System with Mutual Interference and Impulses

A class of Holling type II predator-prey systems with mutual interference and impulses is presented. Sufficient conditions for the permanence, extinction, and global attractivity of system are obtained. The existence and uniqueness of positive periodic solution are also established. Numerical simulations are carried out to illustrate the theoretical results. Meanwhile, they indicate that dynamics of species are very sensitive with the period matching between species’ intrinsic disciplinarians and the perturbations from the variable environment. If the periods between individual growth and impulse perturbations match well, then the dynamics of species periodically change. If they mismatch each other, the dynamics differ from period to period until there is chaos.