APPROXIMATE POWER OF HETEROSCEDASTICITY TEST IN NONLINEAR MODELS WITH ARIMA（0,1,0） ERRORS

This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power calculations for the score test of heteroscedasticity in European rabbit data （Ratkowsky, 1983）. Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.

Complex Dynamics Caused by Torus Bifurcation in Power Systems

Torus bifurcation is a relatively complicated bifurcation caused by a pair of complex conjugate Floquet multipliers coming out of unit circle on the Poincare section. A three-bus system is employed to reveal the relationship between torus bifurcation and some complex dynamics. Based on theoretical analysis and simulation studies, it is found that torus bifurcation is a typical route to chaos in power system. Some complex dynamics usually occur after a torus bifurcation, such as self-organization, deep bifurcations, exquisite structure, coexistence of chaos and divergence. It is also found that chaos has close relationship with various instability scenarios of power systems. Studies of this paper are helpful to understand the mechanism of torus bifurcation in power system and relationship of chaos and power system instabilities.

FINITE TIME BLOW UP OF THE SOLUTIONS TO BOUSSINESQ EQUATION WITH LINEAR RESTORING FORCE AND ARBITRARY POSITIVE ENERGY

Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are derived. The results are valid for initial data with arbitrary high positive energy. The proofs are based on the concave method and new sign preserving functionals.

Double Reduction and Exact Solutions of Zakharov–Kuznetsov Modified Equal width Equation with Power Law Nonlinearity via Conservation Laws

The conservation laws for the （1＋2）-dimensional Zakharov-Kuznetsov modified equal width （ZK-MEW） equation with power law nonlinearity are constructed by using Noether＇s approach through an interesting method of increasing the order of this equation. With the aid of an obtained conservation law, the generalized double reduction theorem is applied to this equation. It can be shown that the reduced equation is a second order nonlinear ODE. FinaJ1y, some exact solutions for a particular case of this equation are obtained after solving the reduced equation.

Parametric characteristic of the random vibration response of nonlinear systems

Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.

Investigation of ellipticity and pump power in a passively mode-locked fiber laser using the nonlinear polarization rotation technique

An elliptical initial polarization state is essential for generating mode-locked pulses using the nonlinear polarization rotation technique. In this work, the relationship between the ellipticity ranges capable of maintaining mode-locked operation against different pump power levels is investigated. An increasing pump power, in conjunction with minor adjustments to the polarization controller＇s quarter waveplate, results in a wider ellipticity range that can accommodate mode-locked operation. Other parameters such as noise, pulsewidth, and average output power are also observed to vary as the ellipticity changes.

Improving the Performance of DC Microgrids by Utilizing Adaptive Takagi-Sugeno Model Predictive Control

In naval direct current(DC)microgrids,pulsed power loads(PPLs)are becoming more prominent.A solar sys-tem,an energy storage system,and a pulse load coupled directly to the DC bus compose a DC microgrid in this study.For DC mi-crogrids equipped with sonar,radar,and other sensors,pulse load research is crucial.Due to high pulse loads,there is a possibility of severe power pulsation and voltage loss.The original contribution of this paper is that we are able to address the nonlinear problem by applying the Takagi-Sugeno(TS)model formulation for naval DC microgrids.Additionally,we provide a nonlinear power observer for estimating major disturbances affecting DC microgrids.To demonstrate the TS-potential,we examine three approaches for mitigating their negative effects:instantaneous power control(IPC)control,model predictive control(MPC)formulation,and TS-MPC approach with compensated PPLs.The results reveal that the TS-MPC approach with adjusted PPLs effectively shares power and regulates bus voltage under a variety of load conditions,while greatly decreasing detrimental impacts of the pulse load.Additionally,the comparison confirmed the efficiency of this technique.Index Terms-DC microgrids(MG),model predictive control(MPC),pulsed power loads(PPLs),nonlinear power observer,Takagi-Sugeno(TS)fuzzy model.

On Some Nonlinear Integral and Discrete Inequalitites Related to Ou-Iang's Inequality

Nonlinear integral and discrete inequalities are obtained. which are related to some recent results of B. C. Pachpatte in [1] given therein as generalizations of Ou-Iang’s integral inequality[2]. As special cases, some new inequalities with the power nonlinearity are derived from the main results. To show the contribution of our results, boundedness of solutions to certain nonlinear difference equation is also considered.