Oscillation Criteria Research Articles

Enhanced Oscillation Criteria for Non-Canonical Second-Order Advanced Dynamic Equations on Time Scales

This study aims to establish novel iterative oscillation criteria for second-order half-linear advanced dynamic equations in non-canonical form. The results extend and enhance recently established criteria for this type of equation by various authors and also encompass the classical criteria for related ordinary differential equations. Our methodology involves transforming the non-canonical equation into its corresponding canonical form. The inherent symmetry of these canonical forms plays a pivotal role in deriving our new criteria. By employing techniques from the theory of symmetric differential equations and utilizing symmetric functions, we establish precise conditions for oscillation. Several illustrative examples highlight the accuracy, applicability, and versatility of our results.

A new integrated modelling and control of ternary pumped storage hydro power generation for small signal stability studies

Pumped storage hydro power generation (PSHPG), a reliable renewable energy source with an energy storage feature, can impart efficient damping torque to power system oscillations to improve small signal stability with appropriate modelling and additional compensation through the governor. But ternary PSHPG (T-PSHPG) has the unique feature of hydraulic short circuit (HSC) mode, where both pumping and generating modes operate simultaneously. This study presents a novel fourth-order modified Heffron Phillips (MHP) model of T-PSHPG in coordination with a multi-band Power system stabilizer (MB-PSS) employing 2-way penstock, where primary penstock circulates water from the upper reservoir to the lower reservoir through the turbine and secondary penstock divides primary penstock, thereby creating short-circuit path through the pump. Also, this model includes additional reactive power droop control to maintain the voltage profile. A new state space matrix has been developed for coordinating T-PSHPG in HSC mode with MB-PSS. The control parameters of the proposed coordinated model are set by a new multi-objective differential evolution-improved particle swam optimization (DE-IPSO) algorithm. With variable load, random solar and wind source penetrations, it has been found that the proposed model can provide adequate damping actions. The sensitivity of the proposed model has been observed by varying critical model parameters by ±50 %. For all conditions, the settling time of speed variation is within 2.672 s to 5.951 s and the minimum damping ratio lies within 0.105 to 0.455. The minimum damping ratio is 0.32 and the settling time is found to be 3.1 s for system response subject to sudden solar power variation, which has been observed by shifting system eigenvalues toward the left half of the complex plane. Time and frequency domain parameters with sensitivity analysis predict system oscillations being damped effectively with consistency for the proposed modelling and control strategy. The results are verified in real-time with OPAL-RT real-time digital simulator. It has been justified by the present study that appropriate modelling of T-PSHPG along with coordinated control action provided by MB-PSS can handle critical power system oscillations efficiently and effective damping torque can be imparted in HSC mode.

Functional excitation-inhibition ratio indicates near-critical oscillations across frequencies

Abstract The concept of excitation/inhibition (E/I) balance plays an important role in understanding brain function in health and disease. We recently introduced an algorithm to determine a functional E/I ratio based on the critical brain dynamics that emerge in neuronal networks balancing between order and disorder. Little, however, is known about the frequency specificity of E/I regulation and how to measure it. Here, we optimized the algorithm for measuring functional excitation-inhibition ratio (fE/I) in narrow frequency ranges and validated it on a computational model of critical oscillations and EEG data. In the computational model, we confirmed that fE/I discriminated E/I connectivity differences across a wide range of frequencies (1–150 Hz). Twin EEG data revealed significant genetic influences on fE/I across frequencies, whereas contrasting eyes-open and -closed EEG indicated functional changes of fE/I restricted to a subset of alpha and beta oscillations and brain regions. We propose that assessing fE/I with finer frequency resolution will prove useful for understanding the functional role of E/I regulation in a spectrally refined fashion in health and disease.

New oscillatory criteria for third-order differential equations with mixed argument

Abstract In this paper, we offer new technique for investigation of the third-order linear differential equation with mixed argument y ‴ ( t ) + p ( t ) y ( τ ( t ) ) = 0. $$\begin{array}{} \displaystyle y'''(t)+p(t)y(\tau(t))=0. \end{array}$$ (E) We establish new criteria for property A of (E) which fulfill the gap in the oscillation theory.

Investigation of the Oscillatory Behavior of the Solutions of a Class of Third-Order Delay Differential Equations with Several Terms

In this paper, we address the study of the oscillatory properties of the solutions of a class of third-order delay differential equations. The primary objective of this study is to provide new relationships that can be employed to obtain criteria for excluding increasing positive solutions and decreasing positive solutions so that the resulting criteria are easier to apply than other criteria that have appeared in the literature. We have obtained new oscillation criteria that hold up more robustly upon application. Some examples are presented to illustrate the significance of our main findings.

New oscillation criteria of fourth-order neutral noncanonical differential equations

New oscillation criteria of fourth-order neutral noncanonical differential equations

Investigation of the Oscillatory Properties of Fourth-Order Delay Differential Equations Using a Comparison Approach with First- and Second-Order Equations

This paper investigates the oscillatory behavior of solutions to fourth-order functional differential equations (FDEs) with multiple delays and a middle term. By employing a different comparison method approach with lower-order equations, the study introduces enhanced oscillation criteria. A key strength of the proposed method is its ability to reduce the complexity of the fourth-order equation by converting it into first- and second-order forms, allowing for the application of well-established oscillation theories. This approach not only extends existing criteria to higher-order FDEs but also offers more efficient and broadly applicable results. Detailed comparisons with previous research confirm the method’s effectiveness and broader relevance while demonstrating the feasibility and significance of our results as an expansion and improvement of previous results.

Second-Order Noncanonical Delay Differential Equations with Sublinear and Superlinear Terms: New Oscillation Criteria via Canonical Transform and Arithmetic–Geometric Inequality

Second-Order Noncanonical Delay Differential Equations with Sublinear and Superlinear Terms: New Oscillation Criteria via Canonical Transform and Arithmetic–Geometric Inequality

Oscillatory and asymptotic behavior of even-order nonlinear differential equations with mixed neutral terms

Abstract This paper deals with the oscillation and asymptotic behaviour of even order nonlinear differential equations with mixed nonlinear neutral terms. The findings are obtained via utilising an integral criterion as well as a comparison theorem with the oscillatory properties of a first order advanced and/or delay differential equation. We provide novel oscillation criteria that improve, extend, and simplify previously published ones. The results are illustrated by two examples.

Surface light scattering: the capability of precisely measuring the interfacial properties of Newtonian fluids within the capillary wave transition region

This work employs a theoretical power spectrum of the dynamics of surface fluctuations in the frequency domain to elucidate the dissipation of capillary waves of fluids in the near-critical oscillation or transition region, seeking to resolve the problem of large discrepancies in viscosity and surface tension measurements in the region. The frequency-domain analysis approach was suggested, involving the discrete Fourier transform to transform the time domain data to the frequency domain and the fitting algorithm for the power spectrum. A total of three refrigerants, four alkanes and six fatty esters were chosen to examine the approach, with a range of the dimensionless number Y between 1.3 and 101.9. The findings demonstrate that frequency-domain approach is an effective way of dealing with dissipation issues for surface light scattering method when approaching the critical oscillation region, and thus could extend the technique for determining the viscosity and surface tension of Newtonian fluids to a sufficient wide viscosity range.

Neutral Emden–Fowler Differential Equation of Second Order: Oscillation Criteria of Coles Type

In this work, we study the asymptotic and oscillatory behavior of solutions to the second-order general neutral Emden–Fowler differential equation (avηxvz′v)′ + qvFxgv = 0, where v≥v0 and the corresponding function z = x + px∘h. Besides the importance of equations of the neutral type, studying the qualitative behavior of solutions to these equations is rich in analytical points and interesting issues. We begin by finding the monotonic features of positive solutions. The new properties contribute to obtaining new and improved relationships between x and z for use in studying oscillatory behavior. We present new conditions that exclude the existence of positive solutions to the examined equation, and then we establish oscillation criteria through the symmetry property between non-oscillatory solutions. We use the generalized Riccati substitution method, which enables us to apply the results to a larger area than the special cases of the considered equation. The new results essentially improve and extend previous results in the literature. We support this claim by applying the results to an example and comparing them with previous findings. Moreover, the reduction of our results to Euler’s differential equation introduces the well-known sharp oscillation criterion.

Combustion and extinction characteristics of an ethanol pool fire perturbed by low–frequency acoustic waves

To study combustion and extinction characteristics of flames perturbed by acoustic waves, the evolution of the shape of the pool fire, mass loss rate (ma′) of fuel, and mechanisms of extinction of the flames under acoustic perturbations were studied. Moreover, based on parameters of combustion characteristics of flames, parametric models of ma′ and flame extinction were developed. The research results demonstrate that the shapes of unperturbed flames change during combustion, however, when perturbed by acoustic waves, the flame shapes become irregular and the flame fronts become disorderly. Compared with the combustion of unperturbed flames, ma′ is increased under acoustic perturbation. There are upper and lower limits for the change of ma′, so the models of upper and lower limits of ma′ in the concentrated area were established. Low–frequency acoustic waves tend to extinguish the pool fire, and the increased distance of acoustic response and acoustic source power can promote flame extinction. A linear relationship between flame extinction and acoustic frequency was semi-quantitatively characterized by a modified Damköhler (Da*) number. Based on the critical oscillation–induced displacement for extinguishing a pool fire, local acoustic parameters were characterized, and a critical model for local displacement during the extinction of the pool fire was established.

On the Oscillation of a Class of Conformable Schrodinger Equations

In this article, we have derived a new oscillation criteria for a class of conformable Schrodinger equations. Based on the generalized Riccati technique, the results were obtained here. Also we have extended the Hartman-Winter oscillation criteria to conformable Schrodinger equation.

New oscillation criteria for first-order differential equations with general delay argument

New oscillation criteria for first-order differential equations with general delay argument

تذبذب نموذج تكون الدم النبضي مع معاملات موجبة وسالبة

في هذا البحث تم بحث مشكلة الحلول المتذبذبة لنموذج تكون الدم النبضي ذات المعاملات الموجبة والسالبة. هناك العديد من العمليات التطورية ، والتي كثيرًا ما تواجه تحولات دراماتيكية في أوقات محددة وتكون حساسة للاضطرابات قصيرة المدى. نتيجة لذلك ، نقوم ببناء العديد من معايير التذبذب التي تكون إما جديدة تمامًا أو تعزز العديد من النتائج الحديثة في الأدبيات. نقدم أيضًا أمثلة توضيحية لكيفية تأثير النبضات على الحلول المتذبذبة لنموذج تكوين الدم.

Some New Oscillation Criteria for Euler-Bernoulli Beam Equations with Damping Term

Some New Oscillation Criteria for Euler-Bernoulli Beam Equations with Damping Term

Oscillation criteria for the second-order linear advanced differential equation

New oscillatory criteria are established for the second-order linear advanced differential equation. Riccati’s technique and suitable estimates of non-oscillatory solutions are used for the proof of the results obtained. The presented criteria, in a certain sense, generalize the known ones.

An improved oscillation theorem for nonlinear delay differential equations

In this article, we establish a new oscillation criterion for all solutions of first order nonlinear delay differential equations. The main result improves well-known oscillation conditions in the literature. Besides, an example is presented to prove the importance of the main theorem.

Oscillatory criteria of noncanonical even-order differential equations with a superlinear neutral term

The oscillatory behavior of solutions of an even-order differential equation with a superlinear neutral term is considered using Riccati and generalized Riccati transformations, the integral averaging technique, and the theory of comparison. New sufficient conditions are established in the noncanonical case. An example is given to support our results.

Some Oscillatory Criteria for Second-Order Emden–Fowler Neutral Delay Differential Equations

In this paper, by using the Riccati transformation and integral inequality technique, we establish several oscillation criteria for second-order Emden–Fowler neutral delay differential equations under the canonical case and non-canonical case, respectively. Compared with some recent results reported in the literature, we extend the range of the neutral coefficient. Therefore, our results generalize to some of the results presented in the literature. Furthermore, several examples are provided to illustrate our conclusions.