THE LIMIT CYCLES AND HOPF BIFURCATION OF A CLASS OF SIMPLIFIED HOLLING TYPE-IV PREDATOR-PREY SYSTEM WITH LINEAR STATE FEEDBACK

In this paper, a class of simplified Type-IV predator-prey system with linear state feedback is investigated. We prove the boundedness of the positive solutions to this system, and analyze the quality of the equilibria and the existence of limit cycles of the system surrounding the positive equilibra. By Hopf bifurcation theory, the result of having two limit cycles to the system is obtained.     

Decay and nonexistence of global solutions of a quasilinear riser equation

We study qualitative properties of a quasilinear wave equation of fourth order that models the mechanical vibrations of a marine riser. Our analysis characterizes global and nonglobal solutions with respect to the norm of some Hilbert space, if energy is strictly less than the potential well depth. We employ invariant sets to show our results. In particular, we show that globality implies exponential decay to zero, and nonglobality is due to blow up. Both results are shown with respect to the norm of the solution in the Hilbert space. Copyright © 2009 John Wiley & Sons, Ltd.     

随机脉冲泛函微分方程的{\boldmath p}阶矩有界性

随机脉冲泛函微分方程是一个具有广泛应用前景的数学模型. 该文利用带Razumikhin条件的Liapunov直接法和比较原理, 得到了随机脉冲泛函微分方程的解的一致(一致且最终、一致且一致最终) p阶矩有界的充分条件, 其中在获得一致有界性和一致最终有界性时, 对dV(t, x(t))/dt 的限制条件也较少, 因此研究结果非常便于应用.     

带多项式相位的高维振荡积分算子的有界性

考虑如下的振荡积分算子:T_(m,k,n)f(x):=∫_(R~n)e~(i(x_1~2+…+x_n~2))~m(y_1~2+…+y_n~2)~kf(y)dy,其中函数f为定义在R~n上的Schwartz函数,并且满足m,k0.本文给出算子T_(m,k,n).从L~p(R~n)(1≤p∞)到L~q(R~n)有界的一个充分必要条件.此外,我们还证明了算子T_(m,k,n)把L~1(R~n)映到C_0(R~n).     

Boundedness in a four‐dimensional attraction‐repulsion chemotaxis system with logistic source

In this paper, we study the attraction‐repulsion chemotaxis system with logistic source: u_t = Δu−χ∇·(u∇v)+ξ∇·(u∇w)+f(u), 0 = Δv−βv+αu, 0 = Δw−δw+γu, subject to homogeneous Neumann boundary conditions in a bounded and smooth domain , where χ,α,ξ,γ,β, and δ are positive constants, and is a smooth function satisfying f(s) ≤ a−bs^3/2 for all s ≥ 0 with a ≥ 0 and b > 0. It is proved that when the repulsion cancels the attraction (ie, ξγ=χα), for any nonnegative initial data , the solution is globally bounded. This result corresponds to the one in the classical 2‐dimensional Keller‐Segel model with logistic source bearing quadric growth restrictions.     

Qualitative theory for Volterra difference equations

We investigate l^p boundedness, the topological structure of solutions set and the asymptotic periodicity of Volterra functional difference equations. The theoretical results are complemented with a set of applications.     

On Stability and Trajectory Boundedness in Mean-square Sense for ARMA Processes

Abstract For the multidimensional ARMA system A(z)y_k=C(z)w_k it is shown that stability(det A(z)≠0,z:│z│≤1)of A(z) is equivalent to the trajectory boundedness in the mean square sense(MSS)which,as a rule,is a consequence of a successful stochastic adaptive control leading the closed-loop of an ARMAXsystem to a steady state ARMA system.In comparison with existing results the stability condition imposed onC(z)is no longer needed.The only structural requirement on the system is that det A(z) and det C(z) have nounstable common factor.     

Divergent Cesàro and Riesz means of Jacobi and Laguerre expansions

We show that for below certain critical indices there are functions whose Jacobi or Laguerre expansions have almost everywhere divergent Cesàro and Riesz means of order .

     

Singular integrals with rough kernels along real-analytic submanifolds in

mapping properties will be established in this paper for singular Radon transforms with rough kernels defined by translates of a real-analytic submanifold in .

     

ON THE STABILITY AND BOUNDEDNESS OFSOLUTIONS FOR THE RETORDED LIENARD-TYPE EQUATION

1IntroductionConsidertheretardedLi6nard--typeequationwherehisanonnegativeconstant,fitfi,WandgarecontinuousfunctionsonR.Recently,theboundedness,stability,oscillationandperiodicityofsolutionsofwhichisEq.(1)withoutdelayandW(x)=0,hasbeenwidelyinvestigated(of[1-5]).Clearly,iffi(x)=f(x),f200=0,W(x)=0,Eq.(1)isreducedtothewell-knownretardedLi6nardequationIn1963,Krasovskii[6]gaveasufficientconditionoftheuniformasymptoticstabilityofthezerosolutionforEq.(3).Hisworkcausedmuchinterest,itisseenbythewor…