时滞在具有Ivlev型功能反应函数的捕食者-食饵扩散系统中的作用

该文研究了时滞对一个带Neumann边值的捕食者-食饵的反应扩散系统的影响.通过对特征根的分析,讨论了非负平衡解的稳定性和Hopf分支的存在性.应用规范型方法和中心流形理论,文章讨论了Hopf分支周期解的稳定性和分支方向。     

A good approximation of modulated amplitude waves in Bose–Einstein condensates

In this paper, we present a perturbation method that utilizes Hamiltonian perturbation theory and averaging to analyze spatio-temporal structures in Gross–Pitaevskii equations and thereby investigate the dynamics of modulated amplitude waves (MAWs) in quasi-one-dimensional Bose–Einstein condensates with mean-field interactions. A good approximation for MAWs is obtained. We also explore dynamics of BECs with the nonresonant external potentials and scatter lengths varying periodically in detail using Hamiltonian perturbation theory and numerical simulations.     

Error analysis and lattice improvement for the C-ADS Injector- I

The injector Scheme- 1 （or Injector- I ） of the C-ADS linac is a 10 mA 10 MeV proton linac working in C／V mode. It is mainly comprised of a 3.2 MeV room-temperature 4-vane RFQ and twelve superconducting single-spoke cavities housed in a long cryostat. Error analysis including alignment and field errors, and static and dynamic ones for the illjector are presented. Based on detailed numerical simulations, an orbit correction scheme has been designed, which shows that with correction the rms residual orbit errors can be controlled within 0.3 mm and a beam loss rate of 1.7× 10-6 is obtained. To reduce the beam loss rate further, an improved lattice design for the superconducting spoke cavity section has been studied.     

Global residue harmonic balance method to periodic solutions of a class of strongly nonlinear oscillators

A new approach, namely the global residue harmonic balance method, was advanced to determine the accurate analytical approximate periodic solution of a class of strongly nonlinear oscillators. A class of nonlinear jerk equation containing velocity-cubed and velocity times displacements-squared was taken as a typical example. Unlike other harmonic balance methods, all the former residual errors are introduced in the present approximation to improve the accuracy. Comparison of the result obtained using this approach with the exact one and simplicity and efficiency of the proposed procedure. The method can be easily extended to other strongly nonlinear oscillators.     

The Periodic Solutions of a Nonhomogeneous String with Dirichlet-Neumann Condition

This paper deals with the existence of periodic solutions of a nonhomogeneous string with Dirichlet-Neumann condition. The authors consider the case that the period is irrational multiple of space length and prove that for some irrational number, zero is not the accumulation point of the spectrum of the associated linear operator. This result can be used to prove the existence of the periodic solution avoid using Nash-Moser iteration.     

Estimating Mahler measures using periodic points for the doubling map

The Mahler measure m(P)$m\left(P\right)$ of a polynomial P$P$ is a numerical value which is useful in number theory, dynamical systems and geometry. In this article we show how this can be written in terms of periodic points for the doubling map on the unit interval. This leads to an interesting algorithm for approximating m(P)$m\left(P\right)$ which we illustrate with several examples.     

Periodic solutions in an array of coupled FitzHugh–Nagumo cells

We analyse the dynamics of an array of N²$N^2$ identical cells coupled in the shape of a torus. Each cell is a 2-dimensional ordinary differential equation of FitzHugh–Nagumo type and the total system is _ZN×_ZN${\mathbb{Z}}_N\times {\mathbb{Z}}_N$-symmetric. The possible patterns of oscillation, compatible with the symmetry, are described. The types of patterns that effectively arise through Hopf bifurcation are shown to depend on the signs of the coupling constants, under conditions ensuring that the equations have only one equilibrium state.