Local Bifurcation of a Thin Rectangle Plate with the Friction Support Boundary

The dynamical equations of a thin rectangle plate subjected to the friction support boundary and its plane force are established in this paper. The local bifurcation of this system is investigated by using L S method and the singularity theory. The Z 2 bifurcation in non degenerate case is discussed. The local bifurcation diagrams of the unfolding parameters and the bifurcation response characters referred to the physical parameters of the system are obtained by numerical simulation. The results of the computer simulation are coincident with the theoretical analysis and experimental results.

Stability and local bifurcation of parameter-excited vibration of pipes conveying pulsating fluid under thermal loading

The parametric excited vibration of a pipe under thermal loading may occur because the fluid is often transported heatedly. The effects of thermal loading on the pipe stability and local bifurcations have rarely been studied. The stability and the local bifurcations of the lateral parametric resonance of the pipe induced by the pulsating fluid velocity and the thermal loading are studied. A mathematical model for a simply supported pipe is developed according to the Hamilton principle. Two partial differential equations describing the lateral and longitudinal vibration are obtained. The singularity theory is utilized to anMyze the stability and the bifurcation of the system solutions. The transition sets and the bifurcation diagrams are obtained both in the unfolding parameter space and the physical parameter space, which can reveal the relationship between the thermal field parameter and the dynamic behaviors of the pipe. The frequency response and the relationship between the critical thermal rate and the pulsating fluid velocity are obtained. The numerical results demonstrate the accuracy of the single-mode expansion of the solution and the stability and local bifurcation analyses. It also confirms the existence of the chaos. The presented work can provide valuable information for the design of the pipeline and the controllers to prevent the structural instability.

STABILITY AND LOCAL BIFURCATION IN A SIMPLY-SUPPORTED BEAM CARRYING A MOVING MASS

The stability and local bifurcation of a simply-supported flexible beam （Bernoulli- Euler type） carrying a moving mass and subjected to harmonic axial excitation are investigated. In the theoretical analysis, the partial differential equation of motion with the fifth-order nonlinear term is solved using the method of multiple scales （a perturbation technique）. The stability and local bifurcation of the beam are analyzed for 1/2 sub harmonic resonance. The results show that some of the parameters, especially the velocity of moving mass and external excitation, affect the local bifurcation significantly. Therefore, these parameters play important roles in the system stability.

Local Bifurcation of Critical Periods for a Class of Liénard Equations

In this paper, we study the local bifurcation of critical periods near the nondegenerate center （the origin） of a class of Li@nard equations with degree 2n, and prove that at most 2n - 2 critical periods （taken into account multiplicity） can be produced from a weak center of finite order. We also prove that it can have exactly 2n - 2 critical periods near the origin.

The Local Bifurcation and Stability of Nontrivial Steady States of a Logistic Type of Chemotaxis

Chemotaxis is a type of oriented movement of cells in response to the concentration gradient of chemical substances in their environment. We consider local existence and stability of nontrivial steady states of a logistic type of chemotaxis. We carry out the bifurcation theory to obtain the local existence of the steady state and apply the expansion method on the chemotaxis to investigate the bifurcation direction. Moreover, by applying the bifurcation direction, we obtain the bifurcating steady state is stable when the bifurcation curve turns to right under certain conditions.

Local Hopf bifurcation and global existence of periodic solutions in TCP system

This paper investigates the dynamics of a TCP system described by a first- order nonlinear delay differential equation. By analyzing the associated characteristic transcendental equation, it is shown that a Hopf bifurcation sequence occurs at the pos- itive equilibrium as the delay passes through a sequence of critical values. The explicit algorithms for determining the Hopf bifurcation direction and the stability of the bifur- cating periodic solutions are derived with the normal form theory and the center manifold theory. The global existence of periodic solutions is also established with the method of Wu （Wu, J. H. Symmetric functional differential equations and neural networks with memory. Transactions of the American Mathematical Society 350（12）, 4799-4838 （1998））.

Stability of the Bifurcation Solutions for a Predator-Prey Model

The bifurcation solution of the nonnegative steady state of a reaction diffusion system was investigated. The combination of the sturm type eigenvalue and the theorem of bifurcation was used to study the local coexistence solutions, and obtain the stability of bifurcation solutions. The system model describes predator prey interaction in an unstirred chemostat.

Research on a bifurcation location algorithm of a drainage tube based on 3D medical images

Based on patient computerized tomography data,we segmented a region containing an intracranial hematoma using the threshold method and reconstructed the 3D hematoma model.To improve the efficiency and accuracy of identifying puncture points,a point-cloud search arithmetic method for modified adaptive weighted particle swarm optimization is proposed and used for optimal external axis extraction.According to the characteristics of the multitube drainage tube and the clinical needs of puncture for intracranial hematoma removal,the proposed algorithm can provide an optimal route for a drainage tube for the hematoma,the precise position of the puncture point,and preoperative planning information,which have considerable instructional significance for clinicians.