食饵-捕食者相互作用系统的定性分析

本文运用Liapunov第二方法，研究了食饵-捕食者系统｛x^·=f(x)-φ(x)τ(y)y^·=-eh(y) kh(y)φ(z)正平衡点的稳定性，并利用Poincare-Bendixon环域定理及张芷芬唯一性定理，论证了在R2^ =｛(x,y):x>0,y>0｝内极限环的存在唯一性及其稳定性。     

Linear Rayleigh-Taylor instability analysis of double-shell Kidder＇s self-similar implosion solution

This paper generalizes the single-shell Kidder＇s self-similar solution to the double-shell one with a discontinuity in density across the interface. An isentropic implosion model is constructed to study the Rayleigh-Taylor instability for the implosion compression. A Godunov-type method in the Lagrangian coordinates is used to compute the one-dimensional Euler equation with the initial and boundary conditions for the double-shell Kidder＇s self-similar solution in spherical geometry. Numerical results are obtained to validate the double-shell implosion model. By programming and using the linear perturbation codes, a linear stability analysis on the Rayleigh-Taylor instability for the double-shell isentropic implosion model is performed. It is found that, when the initial perturbation is concentrated much closer to the interface of the two shells, or when the spherical wave number becomes much smaller, the modal radius of the interface grows much faster, i.e., more unstable. In addition, from the spatial point of view for the compressibility effect on the perturbation evolution, the compressibility of the outer shell has a destabilization effect on the Rayleigh-Taylor instability, while the compressibility of the inner shell has a stabilization effect.