KOITER-BOUNDARY LAYER SINGULAR PERTURBATION METHOD FOR AXIAL COMPRESSED STIFFENED CYLINDRICAL SHELLS

The double singularities induced by bifurcation point and boundary layer in non-dimensionalized nonlinear boundary-layer Karman-Donnell equations for axially compressed stiffened cylindrical shells can be treated by Koiter-boundary layer singular perturbation method in this paper. It is demonstrated that the method has high computing efficiency and accuracy based on the analysis of AS-2 shell, and some new conclusions can be directly obtained from the perturbation formulas which are very well in agreement with experimental phenomenon of axially compressed stiffened cylindrical shells.

Trajectory Tracking of Vertical Take-off and Landing Unmanned Aerial Vehicles Based on Disturbance Rejection Control

We investigate the trajectory tracking problem of vertical take-off and landing(VTOL) unmanned aerial vehicles(UAV), and propose a practical disturbance rejection control strategy. Firstly, the nonlinear error model is established completely by the modified Rodrigues parameters, while considering dynamics of the servo actuators. Then, a hierarchical control scheme is applied to design the translational and rotational controllers based on the time-scale property of each subsystem,respectively. And the linear extended state observer and auxiliary observer are used to deal with the uncertainties and saturation.At last, global stability of the closed-loop system is analyzed based on the singular perturbation theory. Simulation results show the effectiveness of the proposed control strategy.

Time-Delay Effects on Synchronization of Coupled Slow-Fast Systems

Time-delay effects on synchronization features of delay-coupled slow-fast van der Pol systems are investigated in the present paper. The synchronization mechanism of “slow-manifold adjustment” is firstly described on the basis of geometric singular perturbation theory. Then, the impact of time delay on the structure of the slow manifold of synchronized system is obtained by using the method of stability switch, and thus, time-delay effects on synchronization features are stated. It is shown the time delay cannot qualitatively affect the synchronization mechanism, however, it can result in the drift of the optimal coupling strength.

Canard Solutions in a Predator-Prey Model

The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as, fold point, transcritical point, pitchfork point, canard point, are identified;then Hopf bifurcation, relaxation oscillation, together with the canard transition from Hopf bifurcation to relaxation oscillation are discussed.

Truncation Analysis for the Derivative Schrodinger Equation

The truncation equation for the derivative nonlinear Schrodinger equation has been dis- cussed in this paper. The existence of a special heteroclinic orbit has been found by using geometrical singular perturbation theory together with Melnikov's technique.

Analytical Solution to the Density-Gradient Equation for MOS Quantum Tunneling

Engineering-oriented simulations of quantum mechanical tunneling are often based on density-gradient （DG） theory. This paper presents an analytical solution to the DG equation for quantum tunneling through an ultra-thin oxide in a MOS capacitor with an n＋ poly-silicon gate obtained using the method of matched asymptotic expansions. Tunneling boundary conditions extend the approximation into the entire region of the poty-silicon gate, oxide barrier, and substrate. An analytical solution in the form of an asymptotic series is obtained in each region by treating each part of the domain as a separate singular perturbation problem. The solutions are then combined through ＇matching＇ to obtain an approximate solution for the whole domain. Analytical formulae are given for the electrostatic potential and the electron density profiles. The results capture the features of the quantum effects which are quite different from classical physics pre- dictions. The analytical results compare well with exact numerical solutions over a broad range of voltages and different oxide thicknesses. The analytical results predict the enhancement of the quantum tunneling effect as the oxide thickness is reduced.

Solitary Wave Solutions of Delayed Coupled Higgs Field Equation

This paper is devoted to the study of the solitary wave solutions for the delayed coupled Higgs field equation{vtt-uxx-αu+βf*u|u|^(2)-2uv-τu(|u|^(2))x=0 vtt+vxx-β(|u|^(x))xx=0.We first establish the existence of solitary wave solutions for the corresponding equation without delay and perturbation by using the Hamiltonian system method.Then we consider the persistence of solitary wave solutions of the delayed coupled Higgs field equation by using the method of dynamical system,especially the geometric singular perturbation theory,invariant manifold theory and Fredholm theory.According to the relationship between solitary wave and homoclinic orbit,the coupled Higgs field equation is transformed into the ordinary differential equations with fast variables by using the variable substitution.It is proved that the equations with perturbation also possess homoclinic orbit,and thus we obtain the existence of solitary wave solutions of the delayed coupled Higgs field equation.