Moments Of Impulses Research Articles

Attracting sets of impulse-perturbed heat equation in the space of continuous functions

The paper deals with the impulsive infinite-dimensional problem generated by solutions of the thermal conductivity equation under the condition of impulse ”pumping” of heat. Moments of impulses are not fixed and are determined by the amount of total heat in the system. It is proved that such a problem generates impulsive dynamical system in the space of continuous functions and its ω-limits sets are investigated.

Unpredictability in Quasilinear Non-Autonomous Systems with Regular Moments of Impulses

Unpredictability in Quasilinear Non-Autonomous Systems with Regular Moments of Impulses

Mean-square stability of Riemann\u2013Liouville fractional Hopfield\u2019s graded response neural networks with random impulses

In this paper a model of Hopfield’s graded response neural network is investigated. A network whose neurons are subject to a certain impulsive state displacement at random times is considered. The model is set up and studied. The presence of random moments of impulses in the model leads to a change of the solutions to stochastic processes. Also, we use the Riemann–Liouville fractional derivative to model adequately the long-term memory and the nonlocality in the neural networks. We set up in an appropriate way both the initial conditions and the impulsive conditions at random moments. The application of the Riemann–Liouville fractional derivative leads to a new definition of the equilibrium point. We define mean-square Mittag-Leffler stability in time of the equilibrium point of the model and study this type of stability. Some sufficient conditions for this type of stability are obtained. The general case with time varying self-regulating parameters of all units and time varying functions of the connection between two neurons is studied.

P-moment exponential stability of second order differential equations with exponentially distributed moments of impulses

<abstract><p>Differential equations of second order with impulses at random moments are set up and investigated in this paper. The main characteristic of the studied equations is that the impulses occur at random moments which are exponentially distributed random variables. The presence of random variables in the ordinary differential equation leads to a total change of the behavior of the solution. It is not a function as in the case of deterministic equations, it is a stochastic process. It requires combining of the results in Theory of Differential Equations and Probability Theory. The initial value problem is set up in appropriate way. Sample path solutions are defined as a solutions of ordinary differential equations with determined fixed moments of impulses. P-moment generalized exponential stability is defined and some sufficient conditions for this type of stability are obtained. The study is based on the application of Lyapunov functions. The results are illustrated on examples.</p></abstract>

Unpredictable Solutions of Linear Impulsive Systems

We consider a new type of oscillations of discontinuous unpredictable solutions for linear impulsive nonhomogeneous systems. The models under investigation are with unpredictable perturbations. The definition of a piecewise continuous unpredictable function is provided. The moments of impulses constitute a newly determined unpredictable discrete set. Theoretical results on the existence, uniqueness, and stability of discontinuous unpredictable solutions for linear impulsive differential equations are provided. We benefit from the B-topology in the space of discontinuous functions on the purpose of proving the presence of unpredictable solutions. For constructive definitions of unpredictable components in examples, randomly determined unpredictable sequences are newly utilized. Namely, the construction of a discontinuous unpredictable function is based on an unpredictable sequence determined by a discrete random process, and the set of discontinuity moments is realized by the logistic map. Examples with numerical simulations are presented to illustrate the theoretical results.

Energy flows in gesture-speech physics: The respiratory-vocal system and its coupling with hand gestures.

Expressive moments in communicative hand gestures often align with emphatic stress in speech. It has recently been found that acoustic markers of emphatic stress arise naturally during steady-state phonation when upper-limb movements impart physical impulses on the body, most likely affecting acoustics via respiratory activity. In this confirmatory study, participants (N = 29) repeatedly uttered consonant-vowel (/pa/) mono-syllables while moving in particular phase relations with speech, or not moving the upper limbs. This study shows that respiration-related activity is affected by (especially high-impulse) gesturing when vocalizations occur near peaks in physical impulse. This study further shows that gesture-induced moments of bodily impulses increase the amplitude envelope of speech, while not similarly affecting the Fundamental Frequency (F0). Finally, tight relations between respiration-related activity and vocalization were observed, even in the absence of movement, but even more so when upper-limb movement is present. The current findings expand a developing line of research showing that speech is modulated by functional biomechanical linkages between hand gestures and the respiratory system. This identification of gesture-speech biomechanics promises to provide an alternative phylogenetic, ontogenetic, and mechanistic explanatory route of why communicative upper limb movements co-occur with speech in humans.

P-Moment Mittag–Leffler Stability of Riemann–Liouville Fractional Differential Equations with Random Impulses

Fractional differential equations with impulses arise in modeling real world phenomena where the state changes instantaneously at some moments. Often, these instantaneous changes occur at random moments. In this situation the theory of Differential equations has to be combined with Probability theory to set up the problem correctly and to study the properties of the solutions. We study the case when the time between two consecutive moments of impulses is exponentially distributed. In connection with the application of the Riemann–Liouville fractional derivative in the equation, we define in an appropriate way both the initial condition and the impulsive conditions. We consider the case when the lower limit of the Riemann–Liouville fractional derivative is fixed at the initial time. We define the so called p-moment Mittag–Leffler stability in time of the model. In the case of integer order derivative the introduced type of stability reduces to the p–moment exponential stability. Sufficient conditions for p–moment Mittag–Leffler stability in time are obtained. The argument is based on Lyapunov functions with the help of the defined fractional Dini derivative. The main contributions of the suggested model is connected with the implementation of impulses occurring at random times and the application of the Riemann–Liouville fractional derivative of order between 0 and 1. For this model the p-moment Mittag–Leffler stability in time of the model is defined and studied by Lyapunov functions once one defines in an appropriate way their Dini fractional derivative.

A Two-Step Denoising Strategy for Early-Stage Fault Diagnosis of Rolling Bearings

Empirical wavelet transform (EWT) is an adaptive tool for vibration signals processing and has been adopted for fault diagnosis of rolling bearings, while still suffers two weaknesses in detecting the weak, early-stage defects. First, adaptive and robust boundaries determination of the EWT segments is a challenge. Second, vestigial noise and unwanted vibrations still exist in the filtered signal, which may bury the weak fault signature and weaken the detection performance of early-stage faults. In this article, a two-step denoising strategy (TSDS) is proposed for early-stage fault detection, which includes frequency filtering and time-domain denoising steps. In the scheme, an automated EWT segmentation method is proposed for identifying each primary harmonic component; then, EWT-based correlated kurtogram is adopted to optimize the filtering frequency band such that to enhance the signal-to-noise ratio (SNR) of the fault information. Furthermore, the two-layer sliding-correlated kurtosis (TLSCK) algorithm is applied as the second step, which eliminates the vestigial noise and outputs pure periodic pulses, indicating the occurrence moments of the fault impulses. Thus, the weak, early-stage fault signature can be significantly enhanced and detected. A simulation study is conducted and validates the successfulness of the proposed scheme when the SNR is as low as −19 dB. A run-to-failure experiment verifies the effectiveness of the proposed method for weak faults identification, and comparison studies show that the proposed scheme could diagnosis bearing defects at much earlier moment than traditional methods like spectral kurtosis and dyadic wavelet transform.

Caputo Fractional Differential Equations with Non-Instantaneous Random Erlang Distributed Impulses

The p-moment exponential stability of non-instantaneous impulsive Caputo fractional differential equations is studied. The impulses occur at random moments and their action continues on finite time intervals with initially given lengths. The time between two consecutive moments of impulses is the Erlang distributed random variable. The study is based on Lyapunov functions. The fractional Dini derivatives are applied.

Isolation and Identification of Compound Faults in Rotating Machinery via Adaptive Deep Filtering Technique

Compound defects commonly occur on rotating machinery under fatigue and heavy loads, and their fault signatures are coupled and easily buried in strong unwanted vibrations and background noise. The isolation and identification of the compound fault signatures are still a challenge especially when the transient impulses induced from the compound defects share common resonant frequency. In this paper, a data-driven, adaptive deep filtering technique which mainly contains filtering and isolating procedures is proposed for compound faults diagnosis. During the filtering procedure, an empirical wavelet transform (EWT) based correlated kurtogram is presented to adaptively obtain the proper spectral segments for filtering the vibration measurements, such that to enhance the signal-to-noise ratio (SNR) of compound faults in the filtered signals. Subsequently, during the isolation procedure, windowed correlated kurtosis (WCK) which outputs pure periodic pulses indicating the occurrence moments of interested fault impulses is presented to isolate each interested fault mode and to determine the defects number. The performance of the proposed technique is tested on simulated signals and validated via analyzing experimental measurements from high-speed locomotive bearings which suffer multiple damages. The results validate that the proposed method outperforms dyadic wavelet transform and spectral kurtogram in isolating and identifying compound faults in rotating machinery.

Development of Mathematical Algorithm for Seismoacoustic Signals Identification Using Local Geomechanical Control Means

This article reviews a creating of algorithm for the automatic seismoacoustic signals identification. The developed algorithm will be part of the software multi-channel device. The useful signals detection problem from the geomechanical state data stream is solved by determining the moments of impulses beginning and ending. The initial moment of time is determined using fast and slow exponential moving averages, used to smooth out data variations and the characteristic signal-to-noise ratio. The moving average method is used in conjunction with an adaptive threshold, which improves the accuracy of determining the initial moment and takes into account the noise. The last time instant of the useful signal is detected with the help of a cumulative envelope. The time of impulse beginning detection is calculated and terminated when the threshold value is reached. The developed mathematical algorithm allows to identify seismoacoustic signals with sufficient accuracy and is an undemanding hardware resource of the device that allows using it in real time.

Global Mittag—Leffler Synchronization for Neural Networks Modeled by Impulsive Caputo Fractional Differential Equations with Distributed Delays

The synchronization problem for impulsive fractional-order neural networks with both time-varying bounded and distributed delays is studied. We study the case when the neural networks and the fractional derivatives of all neurons depend significantly on the moments of impulses and we consider both the cases of state coupling controllers and output coupling controllers. The fractional generalization of the Razumikhin method and Lyapunov functions is applied. Initially, a brief overview of the basic fractional derivatives of Lyapunov functions used in the literature is given. Some sufficient conditions are derived to realize the global Mittag–Leffler synchronization of impulsive fractional-order neural networks. Our results are illustrated with examples.

Differential equations with random Gamma distributed moments of non-instantaneous impulses and p-moment exponential stability

Abstract Nonlinear differential equations with impulses occurring at random time and acting noninstantaneously on finite intervals are studied.We consider the case when the time where the impulses occur is Gamma distributed. Lyapunov functions are applied to obtain sufficient conditions for the p-moment exponential stability of the trivial solution of the given system.

Asymptotic representation of solutions for second-order impulsive differential equations

We obtain sufficient conditions which guarantee the existence of a solution of a class of second order nonlinear impulsive differential equations with fixed moments of impulses possessing a prescribed asymptotic behavior at infinity in terms of principal and nonprincipal solutions. An example is given to illustrate the relevance of the results.

Effects of variable-time impulses on global exponential stability of Cohen–Grossberg neural networks

We investigate the global exponential stability of Cohen–Grossberg neural networks (CGNNs) with variable moments of impulses using B-equivalence method. Under certain conditions, we show that each solution of the considered system intersects each surface of discontinuity exactly once, and that the variable-time impulsive systems can be reduced to the fixed-time impulsive ones. The obtained results imply that impulsive CGNN will remain stability property of continuous subsystem even if the impulses are of somewhat destabilizing, and that stabilizing impulses can stabilize the unstable continuous subsystem at its equilibrium points. Moreover, two stability criteria for the considered CGNN by use of proposed comparison system are obtained. Finally, the theoretical results are illustrated by two examples.

Impulsive differential equations with Gamma distributed moments of impulses and p-moment exponential stability

Differential equations with impulses at random moments are set up and investigated. We study the case of Gamma distributed random moments of impulses. Several properties of solutions are studied based on properties of Gammma distributions. Some sufficient conditions for p-moment exponential stability of the solutions are given.

P-Moment Exponential Stability of Caputo Fractional Differential Equations with Random Impulses

Fractional differential equations with random impulses arise in modeling real world phenomena where the state changes instantaneously at uncertain moments. Using queuing theory and the usual distribution for waiting time, we study the case of exponentially distributed random variables between two consecutive moments of impulses. The p-moment exponential stability of solutions is defined and studied when the waiting time between two consecutive impulses is exponentially distributed. The argument is based on Lyapunov functions. We discuss both continuous and differentiable Lyapunov functions and Caputo fractional Dini derivatives and Caputo derivatives are applied. Some examples are given to illustrate our results.

A Memristor-Based Lorenz Circuit and Its Stabilization via Variable-Time Impulsive Control

In this paper, an off-the-shelf memristor emulator of the quadratic memristor is developed and applied to a Lorenz circuit. The impulsive stabilization of the chaotic system by variable moments of impulses is investigated. By B-equivalence method, the considered variable-time impulsive system can be reduced to the fixed-time impulsive one. The simulations of the chaotic behavior verify the effectiveness of the emulator-based memristive system. The stability simulations support the validity of the method.

Global attractors of impulsive parabolic inclusions

In this work we consider an impulsive multi-valued dynamical system generated by a parabolic inclusion with upper semicontinuous right-hand side \begin{document}$\varepsilon F(y)$\end{document} and with impulsive multi-valued perturbations. Moments of impulses are not fixed and defined by moments of intersection of solutions with some subset of the phase space. We prove that for sufficiently small value of the parameter \begin{document}$\varepsilon>0$\end{document} this system has a global attractor.

Stability in non-autonomous periodic systems with grazing stationary impacts

This paper examines impulsive non-autonomous periodic systems whose surfaces of discontinuity and impact functions are not depending on the time variable. The W−map which alters the system with variable moments of impulses to that with fixed moments and facilitates the investigations, is presented. A particular linearizion system with two compartments is utilized to analyze stability of a grazing periodic solution. A significant way to keep down a singularity in linearizion is demonstrated. A concise review on sufficient conditions for the linearizion and stability is presented. An example is given to actualize the theoretical results.