Dynamics of SIS model with saturation incidence,infection age and impulsive birth

In this paper, an impulsive birth and infection age SIS epidemic model is studied. Since infection age is an important factor of epidemic progression, we incorporate the infection age into the model. In this model, we analyze the dynamical behaviors of this model and point out that there exists an infection‐free periodic solution that is globally asymptotically stable if R₀<1. When R₁>1, R₂<1, then the disease is permanent. Our results indicate that a large period T of pulse, or a small pulse birth rate p is the sufficient condition for the eradication of the disease. Copyright © 2009 John Wiley & Sons, Ltd.     

MAXIMAL ATTRACTORS FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS OF VISCOUS AND HEAT CONDUCTIVE FLUID

This article is concerned with the existence of maximal attractors in Hi(i=1,2,4) for the compressible Navier-Stokes equations for a polytropic viscous heat conduc-tive ideal gas in bounded annular domains Ωn in Rn(n =2,3).One of the important features is that the metric spaces H(1),H(2),and H(4) we work with are three incomplete metric spaces,as can be seen from the constraints θ0 and u0,with θ and u being absolute temperature and specific volume respectively.For any constants δ1,δ2,···,δ8 verifying some conditions,a sequence of closed subspaces Hδ(i)H(i)(i = 1,2,4) is found,and the existence of maximal(universal) attractors in Hδ(i)(i = 1,2,4) is established.     

Regular Global Attractors of Type Ⅲ Thermoelastic Extensible Beams

For β∈ R,the authors consider the evolution system in the unknown variables u and ααttu+αxxxxu+αxxtα-(β+αxu L22)αxxu=f,αttα-αxxα-αxxtα-αxxtu=0 describing the dynamics of type III thermoelastic extensible beams,where the dissipation is entirely contributed by the second equation ruling the evolution of the thermal displacement α.Under natural boundary conditions,the existence of the global attractor of optimal regularity for the related dynamical system acting on the phase space of weak energy solutions is established.     

THE FINITE DIFFERENCE METHOD FOR DISSIPATIVE KLEIN-GORDON-SCHRODINGER EQUATIONS IN THREE SPACE DIMENSIONS

A fully discrete finite difference scheme for dissipative Klein-Gordon-SchrSdinger equations in three space dimensions is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions and discrete version of Sobolev embedding the- orems, the stability of the difference scheme and the error bounds of optimal order for the difference solutions are obtained in H2 × H2 ×H1 over a finite time interval. Moreover, the existence of a maximal attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.     

Global attractor for the initial-boundary value problems for Ginzburg-Landau equations for atomic Fermi gases near the BCS-BEC crossover

In this paper, we investigate the time-dependent Ginzburg-Landau (TDGL) equations coming from the superfluid atomic Fermi gases near the Feshbach resonance from the fermion-boson model. By the method of a priori estimates, we get the existence of global attractors in the case of BCS-BEC crossover.     

Global attractor for a nonlinear plate equation with supported boundary conditions

In this paper, we consider a two-dimensional nonlinear equation

(∗)     

Exponential attractor and its fractal dimension for a second order lattice dynamical system

We construct an exponential attractor for a second order lattice dynamical system with nonlinear damping arising from spatial discretization of wave equations in Rk. And we obtain fractal dimension of the exponential attractor and its finite-dimensional approximation.     

Global attractor for a class of nonlinear lattices

We consider a class of nonlinear lattices with nonlinear damping

(0.1)     

Map of growth rate of diamond film synthesized by use of flame CVD

Optimum conditions for the flame synthesis of diamond films have been studied by examining effects of the equivalence ratio, ejection velocity, and velocity gradient on the growth rates and morphologies of diamond films. Important factors that can affect growth rates and morphologies of diamond films deposited in the flame are confirmed to be temperature, flow, and species concentration fields. By use of a flat flame burner, these influences are well understood because the flat acetylene/hydrogen/oxygen flame is stabilized in a well-defined stagnation flow field, which can be regarded as one-dimensional field. It is found that the maximum growth rate can be obtained when the equivalence ratio is from 2.45 to 2.50. It has also been confirmed that the growth rate is nearly the same when the velocity gradient is kept constant. This result indicates that the velocity gradient is one of the important parameters that can govern the growth rate of diamond film. Furthermore, in order to obtain universal, optimum conditions for the flame synthesis of diamond films, an attempt has been conducted to make a map of the growth rates, as functions of equivalence ratio and velocity gradient. Although growth rates increase with increasing velocity gradient, excessively high velocity gradients cause decrease in growth rates. It is found that the maximum growth rate can be obtained when the equivalence ratio is around 2.50 and velocity gradient is 4000 s⁻¹.     

Global dynamics of Filippov-type plant disease models with an interaction ratio threshold

A Filippov-type plant disease model is developed by introducing a interaction ratio threshold, the number of susceptible plants infected by per diseased plant, which determines whether control measures including replanting or roguing are carried out. The main purpose of this paper is to give a completely qualitative analysis of the model. By employing Poincaré maps, our analysis reveals rich dynamics including a global attractor bounded by a touching closed orbit, which is convergent in finite time from its outside, a global attractor bounded by two touching closed orbits and a pseudo-saddle, and a globally asymptotically stable pseudo-node. Moreover, we give biological implications of our results in implementing control strategies for plant diseases.