Oscillation Criteria Research Articles

On the Asymptotic Behavior of Class of Third-Order Neutral Differential Equations with Symmetrical and Advanced Argument

In this paper, we aimed to study some asymptotic properties of a class of third-order neutral differential equations with advanced argument in canonical form. We provide new and simplified oscillation criteria that improve and complement a number of existing results. We also show some examples to illustrate the importance of our results.

A review of critical brain oscillations in depression and the efficacy of transcranial magnetic stimulation treatment.

Repetitive transcranial magnetic stimulation (rTMS) and intermittent theta burst stimulation (iTBS) have been proven effective non-invasive treatments for patients with drug-resistant major depressive disorder (MDD). However, some depressed patients do not respond to these treatments. Therefore, the investigation of reliable and valid brain oscillations as potential indices for facilitating the precision of diagnosis and treatment protocols has become a critical issue. The current review focuses on brain oscillations that, mostly based on EEG power analysis and connectivity, distinguish between MDD and controls, responders and non-responders, and potential depression severity indices, prognostic indicators, and potential biomarkers for rTMS or iTBS treatment. The possible roles of each biomarker and the potential reasons for heterogeneous results are discussed, and the directions of future studies are proposed.

Nonlinear Second Order Delay Dynamic Equations on Time Scales: New Oscillatory Criteria

Nonlinear Second Order Delay Dynamic Equations on Time Scales: New Oscillatory Criteria

On Pseudo-state Matrices of Fractional-Order Multi-frequency Oscillators: A Routh Array Based Oscillatory Criterion and Harmonic Preserving Transformations

On Pseudo-state Matrices of Fractional-Order Multi-frequency Oscillators: A Routh Array Based Oscillatory Criterion and Harmonic Preserving Transformations

Enhanced criteria for detecting oscillations in neutral delay Emden-Fowler differential equations

In this article, we present new oscillation criteria for a specific class of second-order differential equations known as neutral delay Emden-Fowler equations. By utilizing advanced mathematical techniques, we are able to derive conditions that are more accurate and efficient than previous methods. Furthermore, our results also simplify the process of identifying oscillations in these types of equations. Our findings have important implications for various fields such as engineering, physics and mathematics, where these equations are widely used to model dynamic systems. Additionally, We have also highlighted some illustrative examples to further demonstrate the applicability and potential of our results.

Oscillation criteria for fractional differential equations with a distributed delay

Oscillation criteria for fractional differential equations with a distributed delay

Forced oscillation suppression using extended virtual synchronous generator in a low-Inertia microgrid

Effects of forced oscillations (FOs) in well-damped power systems are relatively smaller than those of microgrids (MGs) in which the severity of the FOs may be intensified by converter interfaced generators (CIGs). According to the distinct system characteristics, the FOs in MGs will be challenging problems in future research topics. Without proper controls of the CIGs, the FOs may be exhibited extremely higher amplitude, resulting in the MG instability. Such influences will be exacerbated in a low-inertia MG, which can trigger critical frequency oscillation and system collapse. This paper introduces an extended virtual synchronous generator (VSG) with virtual forced components to attenuate the dynamic FO effects in the presence of a low-inertia MG. Contrastive scenarios, i.e., periodic, combined, full sine, and high-frequency FOs are conducted to validate the performances of VSG control in both stand-alone and interconnected MG environments. Numerical results verify that the extended VSG control provides promising benefits in a low-inertia MG not only for the sake of MG stability improvement but also the further FO suppression.

New Criteria on Oscillatory Behavior of Third Order Half-Linear Functional Differential Equations

This paper deals with some new criteria for the oscillation of third order half-linear differential equations. The purpose of the present paper is the linearization of equation 1.1 in the sense that we would deduce oscillation of studied equation from that of the linear form and to provide new oscillation criteria via comparison with first order equations whose oscillatory behavior are known. The obtained results are new, improve and correlate many of the known oscillation criteria appeared in the literature for equation 1.1. The results are illustrated by some examples.

Interface shape dependent interference patterns of NbSe2 heterostructure Josephson junctions

The superconducting critical current oscillations as a function of magnetic field were previously observed in heterostructure Josephson junctions fabricated by twisting and stacking superconducting van der Waals materials. The interference patterns, however, are often distorted. Here, we report a model for understanding the shape of oscillation patterns in heterostructure Josephson junctions. To this end, we fabricated Josephson junctions by stacking two bulk superconducting $2H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$ flakes on top of each other. We were able to control the junction fabricated to be either diffusive or clean by varying the temperature during the stacking process. The measured magnetic field dependence of the critical current exhibits either a Gaussian decay or a clear oscillatory pattern with maxima and minima. We identify the shape of the interference patterns not only depends on the type of junction; they are also strongly dictated by field orientation and interface geometry. This is a consequences of the fact that heterostructure junctions often have inhomogeneous widths that extend along the field direction. We calculate the expected interference pattern from the junction geometry by applying our model and find excellent agreement to our experimental data.

An Improved Oscillation Result for a Class of Higher Order Non-canonical Delay Differential Equations

In this work, by obtaining a new condition that excludes a class of positive solutions of a type of higher order delay differential equations, we were able to construct an oscillation criterion that simplifies, improves and complements the previous results in the literature. The adopted approach extends those commonly used in the study of second-order equations. The simplification lies in obtaining an oscillation criterion with two conditions, unlike the previous results, which required at least three conditions. In addition, we illustrate the improvement with the new criterion, applying it to some examples and comparing the results obtained with previous results in the literature.

High-Order Nonlinear Functional Differential Equations: New Monotonic Properties and Their Applications

We provide streamlined criteria for evaluating the oscillatory behavior of solutions to a class of higher-order functional differential equations in the non-canonical case. We use a comparison approach with first-order equations that have standard oscillation criteria. Normally, in the non-canonical situation, the oscillation test requires three independent conditions, but we provide criteria with two-conditions without checking the additional conditions. Lastly, we give examples to highlight the significance of the findings.

Oscillatory Properties of Fourth-Order Advanced Differential Equations

This paper presents a study on the oscillatory behavior of solutions to fourth-order advanced differential equations involving p-Laplacian-like operator. We obtain oscillation criteria using techniques from first and second-order delay differential equations. The results of this work contribute to a deeper understanding of fourth-order differential equations and their connections to various branches of mathematics and practical sciences. The findings emphasize the importance of continued research in this area.

Oscillation Criteria for Advanced Half-Linear Differential Equations of Second Order

In this paper, we find new oscillation criteria for second-order advanced functional half-linear differential equations. Our results extend and improve recent criteria for the same equations established previously by several authors and cover the existing classical criteria for related ordinary differential equations. We give some examples to illustrate the significance of the obtained results.

Modification of adapted Riccati equation and oscillation of linear and half-linear difference equations

Applying a modification of the adapted Riccati technique, we introduce a new type of oscillation criteria for generalizations of the Euler half-linear difference equation. Our main criterion is new in many cases. This fact is documented by corollaries and examples. In particular, we obtain new results for linear equations.

Properties of second order differential equations with advanced and delay argument

In this paper, we study the second-order linear delay differential equation of the form (E)y′′(t)+p(t)y(τ(t))=0.We establish new oscillation criteria for (1.1), which improve a number of related ones in the literature. Our approach essentially involves establishing stronger monotonicity properties for the positive solutions of (1.1) than those presented in known works. Two main approaches for the investigation of (1.1) will be used, namely a comparison principle with first-order delay differential inequalities and generalization of very effective Koplatadze’s technique. We illustrate the improvement over the known results by applying and comparing our method with the other known results for (1.1).

Design and Optimal Location of Power System Stabilizer in the Multi-Machine Power Network

This paper proposes a damping torque index (DTI) to determine the optimal installation location of the power system stabilizer (PSS) in the multi-machine power network. The proposed index is based on the classical damping torque analysis (CDTA) method for power system low-frequency electro-mechanical (LFEO) analysis. The selection criteria of the PSS location is the maximum magnitude of DTI under normal operating conditions. The CDTA method is used to design PSS, and the phase compensation technique subsequently adjusts the associated parameters. Furthermore, to analyze the power system’s critical oscillation mode, a wide-area damping controller (WADC) is design for the synchronous generator where optimal location of PSS is install. The reduced-order model-based WADC includes time-varying delay in the wide-area signal. The WADC’s input signals from the phasor measurement unit (PMU) and the location of the PMU are selected using geometric measures of observability and WADC parameters design based on the residue approach. The proposed approach is validated in two separate test systems, and modal analysis is carried out on MATLAB software. The simulated results have been validated on the real-time digital simulator (RTDS) RSCAD 5.012. Results obtained on RTDS show that the proposed approach efficiently damps low-frequency electro-mechanical oscillations.

Improved Properties of Positive Solutions of Higher Order Differential Equations and Their Applications in Oscillation Theory

In this article, we present new criteria for testing the oscillation of solutions of higher-order neutral delay differential equation. By deriving new monotonic properties of a class of the positive solutions of the studied equation, we establish better criteria for oscillation. Furthermore, we improve these properties by giving them an iterative character, allowing us to apply the criteria more than once. The results obtained in this paper are characterized by the fact that they do not require the existence of unknown functions and do not need the commutation condition to composition of the delay functions, which are necessary conditions for the previous related results.

Melnikov’s method for controlled stochastic oscillations of a rocking block with fractional derivative

The problem of controlling a rocking block with fractional dissipation so as to prevent it from leaving a prescribed set of bounded oscillations has a number of interesting applications in many scientific and technological fields. This work develops an analytical framework to describe the influence of control on the behavior of a fractionally dissipative rocking block subject to random acceleration of the ground. Control equations are developed and control strategies leading to optimal suppression of instability are asymptotically described under the assumptions of weak dissipation along with a small energy noise. Under these assumptions, the behavior of the block is interpreted as weakly perturbed rocking oscillations close to a generic periodic solution, and the Melnikov approximations are considered as the necessary conditions of instability. The stochastic Melnikov criterion derived in this paper allows for an approximate calculation of an upper bound to the overturning probability as well as to the representation of an optimal control strategy. The Melnikov criterion for stochastic rocking oscillations in the presence of convenient control strategies are derived explicitly for the first time, using an extension of the Melnikov theory to a model with fractional derivative.

Oscillation Test for Second-Order Differential Equations with Several Delays

In this paper, the oscillatory properties of certain second-order differential equations of neutral type are investigated. We obtain new oscillation criteria, which guarantee that every solution of these equations oscillates. Further, we get conditions of an iterative nature. These results complement and extend some beforehand results obtained in the literature. In order to illustrate the results we present an example.

Stability Impacts of an Alternate Voltage Controller (AVC) on Wind Turbines with Different Grid Strengths

This paper studies the stability impact of the alternate voltage controller’s (AVC) low-pass filter (LPF) in a wind turbine’s grid-connected voltage source converter (VSC). A small-signal model of the grid-connected converter is designed with a grid-following synchronization control. More specifically, the non-linear state-space model of the grid-connected converter was developed, including the dynamics of both the inner and outer control loops of the converter, the dynamics of the elements of the electrical system, as well as the digital time delay. An eigenvalue-based stability analysis gives insight into the stability impacts of the outer-loop controllers. It is proven that the cutoff frequency of the AVC’s LPF affects the phase-locked loop (PLL) and AVC bandwidths of instability, as well as the corresponding critical oscillation frequencies. This phenomenon is observed in both weak and strong grids. Consequently, the small-signal stability regions of the PLL and AVC bandwidth can be identified for the range of the AVC’s LPF cutoff frequency under study. The stability regions of the PLL and AVC, which are obtained from the small-signal model, as well as the determined critical oscillation frequencies, are validated through time domain simulations and fast-Fourier transformation (FFT) analysis.