OSCILLATION FOR NONAUTONOMOUS NEUTRAL DYNAMIC DELAY EQUATIONS ON TIME SCALES

The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of all solutions of this equation. Some results extend known results for difference equations when the time scale is the set Z^＋ of positive integers and for differential equations when the time scale is the set IR of real numbers.

Oscillation of Second-order Nonlinear Dynamic Equation on Time Scales

： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many knownresults for second order dynamic equations. Some examples are given to illustrate the main results of this article.

Oscillation of Third-order Delay Dynamic Equations on Time Scales

This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscilla- tion criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.

New Oscillation Criteria of Second-Order Nonlinear Delay Dynamic Equations on Time Scales

By using the generalized Riccati transformation and the integral averaging technique, the paper establishes some new oscillation criteria for the second-order nonlinear delay dynamic equations on time scales. The results in this paper unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation on time scales. The Theorems in this paper are new even in the continuous and the discrete cases.

Bursting oscillations in a hydro-turbine governing system with two time scales

A fast-slow coupled model of the hydro-turbine governing system （HTGS） is established by introducing frequency disturbance in this paper. Based on the proposed model, the performances of two time scales for bursting oscillations in the HTGS are investigated and the effect of periodic excitation of frequency disturbance is analyzed by using the bifurcation diagrams, time waveforms and phase portraits. We find that stability and operational characteristics of the HTGS change with the value of system parameter kd. Furthermore, the comparative analyses for the effect of the bursting oscillations on the system with different amplitudes of the periodic excitation a are carried out. Meanwhile, we obtain that the relative deviation of the mechanical torque mt rises with the increase of a. These methods and results of the study, combined with the performance of two time scales and the fast-slow coupled engineering model, provide some theoretical bases for investigating interesting physical phenomena of the engineering system.

Oscillation Criteria for Third-order NonlinearNeutral Dynamic Equations on Time Scales

Many practical problems, such as those from electronic engineering, mechanicalengineering, ecological engineering, aerospace engineering and so on, need to bedescribed by dynamic equations on time scales, so it is important in theory andpractical significance to study these equations. In this paper, the oscillation andasymptotic behavior of third-order nonlinear neutral delay dynamic equations ontime scales are studied by using generalized Riccati transformation technique, integralaveraging methods and comparison theorems. The main purpose of this paperis to establish some new oscillation criteria for such dynamic equations. The newKamenev criteria and Philos criteria are given, and an example is considered toillustrate our main results.

Forced Oscillation of Neutral Advanced Dynamic Equations with Positive and Negative Coeffcients on Time Scales

In this paper,we consider the forced neutral advanced dynamic equations with positive and negative coeffcients[x(t)-R(t)x(t+r)]+P(t)x(t+τ)△Q(t)x(t+δ)= f(t),t≥t0 on a time scale T.Several suffcient conditions are obtained for the oscillation of the dynamic equations.The main result is illustrated by an example.

SOME OSCILLATION CRITERIA FOR A CLASS OF HIGHER ORDER NONLINEAR DYNAMIC EQUATIONS WITH A DELAY ARGUMENT ON TIME SCALES

In this paper,we establish some oscillation criteria for higher order nonlinear delay dynamic equations of the form[rnφ(⋯r2(r1x^(Δ))^(Δ)⋯)^(Δ)]^(Δ)(t)+h(t)f(x(τ(t)))=0 on an arbitrary time scale T with supT=∞,where n≥2,φ(u)=|u|^(γ)sgn(u)forγ>0,ri(1≤i≤n)are positive rd-continuous functions and h∈C_(rd)(T,(0,∞)).The functionτ∈C_(rd)(T,T)satisfiesτ(t)≤t and lim_(t→∞)τ(t)=∞and f∈C(R,R).By using a generalized Riccati transformation,we give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.The obtained results are new for the corresponding higher order differential equations and difference equations.In the end,some applications and examples are provided to illustrate the importance of the main results.

Oscillation of Higher Order Linear Impulsive Dynamic Equations on Time Scales

In this paper, we will establish some oscillation criteria for the higher order linear dynamic equation on time scale in term of the coefficients and the graininess function. We illustrate our results with an example.

On the Oscillation of Second-Order Nonlinear Neutral Delay Dynamic Equations on Time Scales

Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation on time scales. At the end of this paper, we give an example to illustrate the main results.

Seasonal Characteristics and Interannual Variability of Monthly Scale Low-Frequency Oscillation in a Low-Order Global Spectral Model

Analysis is done of five-year low-pass filtered data by a five-layer low-order global spectral model, indicating that although any non-seasonal external forcing is not considered in the model atmosphere,monthly-scale anomaly takes place which is of remarkable seasonality and interannual variability.Analysis also shows that for the same seasonal external forcing the model atmosphere can exhibit two climatic states,similar in the departure pattern but opposite in sign, indicating that the anomaly is but the manifestation of the adverse states, which supports the theory of multi-equilibria proposed by Charney and Devore(1979) once again.Finally, the source for the low-frequency oscillation of the global atmosphere is found to be the convective heat source / sink inside the tropical atmosphere as discussed before in our study.Therefore, the key approach to the exploration of atmospheric steady low-frequency oscillation and the associated climatic effect lies in the examination of the distribution of convective heat sources / sinks and the variation in the tropical atmosphere.

OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR DYNAMIC EQUATIONS WITH p-LAPLACIAN AND DAMPING

This paper concerns the oscillation of solutions of the second order nonlinear dynamic equation with p-Laplacian and damping（r（t）φ（x^△（t））^△＋p（t）φα（x^△α（t）＋q（t）f（xδ（t））=0on a time scale T which is unbounded above. Sign changes are allowed for the coefficient functions r, p and q. Several examples are given to illustrate the main results.

Forced oscillations and stability analysis of a nonlinear micro-rotating shaft incorporating a non-classical theory

In this paper,the stability and bifurcation analysis of symmetrical and asymmetrical micro-rotating shafts are investigated when the rotational speed is in the vicinity of the critical speed.With the help of Hamilton's principle,nonlinear equations of motion are derived based on non-classical theories such as the strain gradient theory.In the dynamic modeling,the geometric nonlinearities due to strains,and strain gradients are considered.The bifurcations and steady state solution are compared between the classical theory and the non-classical theories.It is observed that using a non-classical theory has considerable effect in the steady-state response and bifurcations of the system.As a result,under the classical theory,the symmetrical shaft becomes completely stable in the least damping coefficient,while the asymmetrical shaft becomes completely stable in the highest damping coefficient.Under the modified strain gradient theory,the symmetrical shaft becomes completely stable in the least total eccentricity,and under the classical theory the asymmetrical shaft becomes completely stable in the highest total eccentricity.Also,it is shown that by increasing the ratio of the radius of gyration per length scale parameter,the results of the non-classical theory approach those of the classical theory.

The Significant Relationship between the Arctic Oscillation (AO) in December and the January Climate over South China

Using NCEP/NCAR reanalysis data, the China rainfall and surface temperature data of the China Meteorological Administration, and the Arctic Oscillation （AO） indices of NOAA, the author investigates relationships between the AO and the precipitation and temperature over China. There exists a good relationship between the AO index in December and the succeeding January precipitation over South China, indicating that when the December AO index is positive （negative）, the January precipitation over South China increases （decreases）. A remarkable negative correlation between the December AO index and the January surface temperature also exists over South China, indicating that when the December AO index is positive （negative）, the January temperature over South China drops （rises）. The occurrence of this anomalous climate is related to the anomalies of the atmospheric circulation systems. The December AO greatly influences circulation anomalies in January. A positive phase of the AO is found to lead to a stronger subtropical jet over the south side from the Iran Plateau to the Tibetan Plateau. Consequently, it results in a deepening pressure trough around the Bay of Bengal, which transports the warm and wet air to South China continuously. The Siberian High in January is stronger and extends farther southeastward. It results in continual cold air at 1000 hPa pouring into South China, inducing low temperature. Cooperating with the trough of the Bay of Bengal, anomalous precipitation occurs over South China. For the negative phase of the December AO, the opposite situation is observed.

Weak wide-band signal detection method based on small-scale periodic state of Duffing oscillator

The conventional Duffing oscillator weak signal detection method, which is based on a strong reference signal, has inherent deficiencies. To address these issues, the characteristics of the Duffing oscillator＇s phase trajectory in a small- scale periodic state are analyzed by introducing the theory of stopping oscillation system. Based on this approach, a novel Duffing oscillator weak wide-band signal detection method is proposed. In this novel method, the reference signal is discarded, and the to-be-detected signal is directly used as a driving force. By calculating the cosine function of a phase space angle, a single Duffing oscillator can be used for weak wide-band signal detection instead of an array of uncoupled Duffing oscillators. Simulation results indicate that, compared with the conventional Duffing oscillator detection method, this approach performs better in frequency detection intervals, and reduces the signal-to-noise ratio detection threshold, while improving the real-time performance of the system.

Modulation of Tropical Cyclogenesis in the Western North Pacific by the Quasi-Biweekly Oscillation

The quasi-biweekly oscillation （QBWO） is the second most dominant intraseasonal mode over the westem North Pacific （WNP） during boreal summer. In this study, the modulation of WNP tropical cyclogenesis （TCG） by the QBWO and its association with large-scale patterns are investigated. A strong modulation of WNP TCG events by the QBWO is found. More TCG events occur during the QBWO＇s convectively active phase. Based on the genesis potential index （GPI）, we further evaluate the role of environmental factors in affecting WNP TCG. The positive GPI anomalies associated with the QBWO correspond well with TCG counts and locations. A large positive GPI anomaly is spatially correlated with WNP TCG events during a life cycle of the QBWO. The low-level relative vorticity and mid-level relative humidity appear to be two dominant contributors to the QBWO-composited GPI anomalies during the QBWO＇s active phase, followed by the nonlinear and potential intensity terms. These positive contributions to the GPI anomalies are partly offset by the negative contribution from the vertical wind shear. During the QBWO＇s inactive phase, the mid-level relative humidity appears to be the largest contributor, while weak contributions are also made by the nonlinear and low-level relative vorticity terms. Meanwhile, these positive contributions are partly cancelled out by the negative contribution from the potential intensity. The contributions of these environmental factors to the GPI anomalies associated with the QBWO are similar in all five flow patterns--the monsoon shear line, monsoon confluence region, monsoon gyre, easterly wave, and Rossby wave energy dispersion associated with a preexisting TC. Further analyses show that the QBWO strongly modulates the synoptic-scale wave trains （SSWs） over the WNP, with larger amplitude SSWs during the QBWO＇s active phase. This implies a possible enhanced （weakened） relationship between TCG and SSWs during the active （inactive） phase. This study improves our understanding of the modulation of WNP TCG by the QBWO and thus helps with efforts to improve the intraseasonal prediction of WNP TCG.

Impacts of SST and SST Anomalies on Low-Frequency Oscillation in the Tropical Atmosphere

Considering the multiscale character of LFO effects of SST on LFO in the tropical atmosphere （low-frequency oscillation） in the tropical atmosphere, the are discussed by using an absolute ageostrophic, baroclinic model. Here, SST effects include sea surface heating and forcing of SST anomalies （SSTAs）. Studies of the influences of sea surface heating on LFO frequency and stability show that sea surface heating can slow the speed of waves and lower their frequency when SST is comparatively low; while higher SST leads to unstable waves and less periods of LFO. Since the impact of a SSTA on ultra-long waves is more evident than that on kilometer-scale waves, long-wave approximation is used when we continue to study the effect of SSTAs. Results indicate that SSTAs can lead to a longer period of LFO, and make waves unstable. In other words, positive （negative） SSTAs can make waves decay （grow）.

Response of Japanese anchovy(Engraulis japonicus)to the Pacific Decadal Oscillation in the Yellow Sea over the past 400 a

Quantitative identification of long-term changes in the abundance of Japanese anchovy(Engraulis japonicus)in the Yellow Sea is particularly important for understanding evolutionary processes of the Yellow Sea ecosystem.Unfortunately,the driving mechanisms of climate variability on the anchovy are still unclear due to the lack of long-term observational data.In this study,we used the fish scale deposition rate in the central Yellow Sea to reconstruct the time series of the anchovy stock over the past 400 a.On this basis,we further explored the impacts of the Pacific Decadal Oscillation(PDO)on the anchovy.Our results show that the anchovy stock is positively correlated with the PDO on a decadal time scale.In addition,anchovy abundance was relatively high during1620–1860 AD(the Little Ice Age,LIA),though in a state of constant fluctuation;anchovy abundance maintained at a relatively low level after~1860 AD.In particular,followed by overfishing since the 1980 s,the anchovy stock has declined sharply.Based on these findings,we infer that fluctuations of the anchovy stock may be regulated by basin-scale“atmosphere–ocean”interactions.Nevertheless,the role of overfishing should not be ignored.

Application of Scale Relativity to the Problem of a Particle in a Simple Harmonic Oscillator Potential

In the present work, Scale Relativity (SR) is applied to a particle in a simple harmonic oscillator (SHO) potential. This is done by utilizing a novel mathematical connection between SR approach to quantum mechanics and the well-known Riccati equation. Then, computer programs were written using the standard MATLAB 7 code to numerically simulate the behavior of the quantum particle utilizing the solutions of the fractal equations of motion obtained from SR method. Comparison of the results with the conventional quantum mechanics probability density is shown to be in very precise agreement. This agreement was improved further for some cases by utilizing the idea of thermalization of the initial particle state and by optimizing the parameters used in the numerical simulations such as the time step and number of coordinate divisions. It is concluded from the present work that SR method can be used as a basis for description the quantum behavior without reference to conventional formulation of quantum mechanics. Hence, it can also be concluded that the fractal nature of space-time implied by SR, is at the origin of the quantum behavior observed in these problems. The novel mathematical connection between SR and the Riccati equation, which was previously used in quantum mechanics without reference to SR, needs further investigation in future work.

Investigating the Effects of Madden-Julian Oscillation on Climate Elements of Iran (1980-2020)

The Madden-Julian Oscillation is one of the large-scale climate change patterns in the maritime tropics,with sub-seasonal time periods of 30 to 60 days affecting tropical and subtropical regions.This phenomenon can cause changes in various quantities of the atmosphere and ocean,such as pressure,sea surface temperature,and the rate of evaporation from the ocean surface in tropical regions.In this research,the effects of Madden-Julian fluctuation on the weather elements of Iran have been investigated with the aim of knowing the effects of different phases in order to improve the quality of forecasts and benefits in territorial planning.At first,the daily rainfall data of 1980-2020 were received from the National Meteorological Organization and quality controlled.Using the Wheeler and Hendon method,the two main components RMM1 and RMM2 were analyzed,based on which the amplitude of the above two components is considered as the main indicator of the intensity and weakness of this fluctuation.This index is based on the experimental orthogonal functions of the meteorological fields,including the average wind levels of 850 and 200 hectopascals and outgoing long wave radiation(OLR)between the latitudes of 20 degrees south and 20 degrees north.The clustering of the 7-day sequence with a component above 1 was used as the basis for clustering all eight phases,and by calculating the abnormality of each phase compared to its long term in the DJF time frame,the zoning of each phase was produced separately.In the end,phases 1,2,7,8 were concluded as effective phases in Iran’s rainfall and phases 3,4,5,6 as suppressive phases of Iran’s rainfall.