Time Decay Rate of Solutions Toward the Viscous Shock Waves under Periodic Perturbations for the Scalar Conservation Law with Nonlinear Viscosity

In this paper,it is proved that the weak solution to the Cauchy problem for the scalar viscous conservation law,with nonlinear viscosity,different far field states and periodic perturbations,not only exists globally in time,but also converges towards the viscous shock wave of the corresponding Riemann problem as time goes to infinity.Furthermore,the decay rate is shown.The proof is given by a technical energy method.

WAVELET BASIS ANALYSIS IN PERTURBEDPERIODIC KdV EQUATION

In the paper by using the spline wavelet basis to constructr the approximate inertial manifold, we study the longtime behavior of perturbed perodic KdV equation.

CHAOS AND BIFURCATION OF PHASE-LOCKING LOOPS UNDER PERIODIC PERTURBATION

This paper discusses the chaos and bifurcation for equation x+cosxx+asinx =ebsint. By use of the Melnikov method the conditions to have the chaotic behavior and to have subharmonic oscillations are given.

Natural coupled orbit-attitude periodic motions in the perturbed-CRTBP including radiated primary and oblate secondary

This study investigated periodic coupled orbit-attitude motions within the perturbed circular restricted three-body problem(P-CRTBP)concerning the perturbations of a radiated massive primary and an oblate secondary.The radiated massive primary was the Sun,and each planet in the solar system could be considered an oblate secondary.Because the problem has no closed-form solution,numerical methods were employed.Nevertheless,the general response of the problem could be non-periodic or periodic,which is significantly depended on the initial conditions of the orbit-attitude states.Therefore,the simultaneous orbit and attitude initial states correction(SOAISC)algorithm was introduced to achieve precise initial conditions.On the other side,the conventional initial guess vector was essential as the input of the correction algorithm and increased the probability of reaching more precise initial conditions.Thus,a new practical approach was developed in the form of an orbital correction algorithm to obtain the initial conditions for the periodic orbit of the P-CRTBP.This new proposed algorithm may be distinguished from previously presented orbital correction algorithms by its ability to propagate the P-CRTBP family orbits around the Lagrangian points using only one of the periodic orbits of the unperturbed CRTBP(U-CRTBP).In addition,the Poincarémap and Floquet theory search methods were used to recognize the various initial guesses for attitude parameters.Each of these search methods was able to identify different initial guesses for attitude states.Moreover,as a new innovation,these search methods were applied as a powerful tool to select the appropriate inertia ratio for a satellite to deliver periodic responses from the coupled model.Adding the mentioned perturbations to the U-CRTBP could lead to the more accurate modeling of the examination environment and a better understanding of a spacecraft's natural motion.A comparison between the orbit-attitude natural motions in the unperturbed and perturbed models was also conducted to show this claim.

Optimization Methods of MPPT Parameters for PV Systems:Review,Classification,and Comparison

To obtain efficient photovoltaic(PV)systems,optimum maximum power point tracking(MPPT)algorithms are inevitable.The efficiency of MPPT algorithms depends on two MPPT parameters,i.e.,perturbation amplitude and perturbation period.The optimization of MPPT algorithms affect both the tracking speed and steady-state oscillation.In this paper,optimization methods of MPPT parameters are reviewed and classified into fixed and variable methods.The fixed MPPT parameters are constant during MPPT performance,and a trade-off should be made between the tracking speed and steady-state oscillation.However,the variable MPPT parameters will be changed to improve both the tracking speed and the steadystate oscillations.Moreover,some of them are simulated,compared,and discussed to evaluate the real contributions of the optimization methods to the MPPT efficiency.Furthermore,significant features of the optimization methods,i.e.,noise immunity,robustness,and computation effort,are investigated.

Elementary Bifurcations of Non-Critical but Non-Hyperbolic Invariant Tori

Consider the time-periodic perturbations of n-dimensional autonomous systems with nonhyperbolic but non-critical closed orbits in the phase space. The elementary bifurcations, such as the saddle-node, transcritical, pitchfork bifurcation to a non-hyperbolic but non-critical invariant torus of the unperturbed systems in the extended phase space (x, t), are studied. Some conditions which depend only on the original systems and can be used to determine the bifurcation structures of these problems are obtained. The theory is applied to two concrete examples.

HOPF-BIFURCATIONS FOR NONHYPERBOLIC INVARIANT TORI

Consider the time-periodic perturbations of an n-dimensional autonomous system with a nonhyperbolic closed orbit in the phase space. By the method of averaging and Floquet theory, the bifurcations of the invariant torus in the extended phase space are studied.